66 CS07 Abstracts

CP1

Modeling Radiative Heat Transfer in MultifilamentFiber Melt-Spinning

The overall goal of this effort is to develop an accuratemodel for the thermal environment downstream of diesso that local heat transfer rates can be realistically de-termined and included in models of fiber drawing. Thegoal is to assess the influence of each heat transfer mode(radiative and convective) at various locations along thespinline and possible interactions between them, under avariety of processing conditions. In the current work we fo-cus on the development of the radiative heat transfer modeland use a simple approach for the convective heat trans-fer contribution. The latter component is calculated aspart of the flow-induced crystallization model of Doufas etal. for a single melt-spun fiber (Journal of Non-NewtonianFluid Mechanics, 92, 27-66, 2000), extended to the mul-tifilament setting with a technique similar to Dutta’s ap-proach (Polym. Eng. Sci., 27, 1050-1058, 1985). A MonteCarlo method is implemented for radiative heat exchangebetween fibers, the spinneret, and the background. Tem-perature variations along individual fibers and the resultinglocal radiative heat transfer are taken into account. Thisapproach allows ready investigation of parametric effectsrelated to geometry and is more realistic than methods ofprior studies. Preliminary results using this model indi-cate that the radiative heat transfer component can havenon-negligible influence on the temperature profile and onthe location of the transition region where crystallizationoccurs in the fiber. Correct prediction of the transition re-gion is critically important for correct modeling of resultingfiber properties. These results will be presented along witha brief discussion of continuing work.

Christopher L. CoxClemson UniversityDept of Mathematical Sciencesclcox@clemson.edu

Zhe ZhangClemson UniversityDepartment of Mathematical Scienceszhez@clemson.edu

David ZumbrunnenClemson UniversityMechanical Engineering Departmentzdavid@clemson.edu

CP1

Active Vibration Control and Model Updating inStructural Dynamics : Linking Control To Industry

The use of active feedback control strategy is a natural wayto stabilize and control dangerous vibrations in vibratingstructures. The existing vibrations control techniques arefraught with numerous computational and engineering dif-ficulties. A novel practical approach for vibration controland related model updating problem overcoming some ofthese difficultes has been developed by the author and hiscollaborators in recent years. These advances will be re-viewed and a brief discussion presented on future reserach.

Biswa N. DattaNorthern Illinois Universitydattab@math.niu.edu

CP1

Portable Performance Optimizations for Vectorand Microprocessor Based Supercomputers

We will present portable performance optimizations basedon a performance history of the fusion code GYRO ontwo diverse architectures, namely a Cray X1E and a CrayXT3 (both single- and dual-core.) The contribution of thiswork will be a summary of the performance enhancementsthat are portable to these machines. Knowing what perfor-mance optimizations are portable across a variety of ma-chines is essential because good performance is more thanfinding the right compiler options.

Mark R. FaheyOak Ridge National Laboratoryfaheymr@ornl.gov

CP2

Toward Fast and Accurate Methods for Dose Com-putation in Radiotherapy

A deterministic Boltzmann transport model for dose calcu-lation in electron radiotherapy is presented. We investigateseveral ways to simplify the deterministic model having twogoals in mind, lower computation times on the one hand,high accuracy and model inherent incorporation of tissueinhomogeneities on the other hand. While being fast, thesecond property is lost in the often used pencil beam mod-els. Several test cases, including the irradiation of a waterphantom, are presented.

Hartmut HenselFraunhofer ITWMKaiserslauternhensel@itwm.fhg.de

Axel Klar, Martin FrankTU KaiserslauternDepartment of Mathematicsklar@mathematik.uni-kl.de, frank@mathematik.uni-kl.de

CP2

Modeling Cell Aggregation in Nonlinear ShearFlow Via the Population Balance Equation

Cell aggregation and adhesion in a nonuniform shear flow isa problem of great interest in many biological studies suchas the study of tumor extravasation during metastasis. Wemodel such a process using the population balance equa-tion. The basic mathematical properties and convergentnumerical scheme are established. We also present numer-ical simulation results on the leukocyte (PMN)-melanomacell emboli formation and subsequent tethering to the vas-cular endothelium (EC).

Jiakou WangDepartment of MathematicsPenn State Universityjiakou@math.psu.edu

Qiang DuPenn State UniversityDepartment of Mathematicsqdu@math.psu.edu

CP2

An Integrative Computational Model of Multicil-

CS07 Abstracts 67

iary Beating and Its Applications

Cilia are microscopic hair-like organelles projecting fromthe cell surface. The study of the motility of cilia andflagella is of great importance in biology and medicine. Bi-ologists revealed that nearly all mammalian cells form acilium. In human body, cilia and flagella are present on al-most all cells including cells in embryo, kidney and brain.Cilia perform essential motile and sensory functions andplay important roles in cell motility of sperm and ovumalong the respective reproductive tracts, transport of mu-cus across respiratory epithelia, cerebrospinal fluid move-ment in the brain, etc. The core of a cilium is called ax-oneme, in which dyneins fueled by ATP are responsible forthe motility of cilia. We present an integrative computa-tional model of multiciliary beating and its applications.The axoneme is modeled by Dillon-Fauci approach whichwas first used in [1] in 2000. Dillon-Fauci axoneme model issimple but very successful in modeling the cilia and spermmotility ([1] Dillon, R. H. and Fauci, L. J. (2000). An inte-grative model of internal axoneme mechanics and externalfluid dynamics in ciliary beating. Journal of TheoreticalBiology, 207:415-430. [2] Dillon, R. H., Fauci, L. J., andOmoto, C. (2003). Mathematical modeling of axonememechanics and fluid dynamics in ciliary and sperm motil-ity. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math.Anal., 10(5):745-757. Progress in partial differential equa-tions (Pullman, WA, 2002). [3] Dillon, R. H., Fauci, L.J., and Yang, X.,(2006) Sperm Motility and MulticiliaryBeating: an Integrative Mechanical Model, Computers andMathematics with Applications, In press. [4] Dillon, R. H.,Fauci, L. J., Omoto, C. and Yang, X. Fluid Dynamic Mod-els of flagellar and ciliary beating, submitted to “Annals ofthe NY Academy of Sciences”.). This model, based uponthe immersed boundary method (Peskin), couples the in-ternal force generation of the molecular motors throughthe passive elastic structure with the external fluid me-chanics governed by the Navier-Stokes equations. In ournumerical results, we show how a single cilium interactswith its neighboring cilia, how viscosity effects its beat-ing frequency, how synchronization phenomena are gen-erated. We also compare the total flow pumped by ciliavs. viscosity, beat frequency. We present the ATP con-sumed at the end of each power and recovery stroke. Atlast I will present the computer simulations for mucocil-iary transport and chlamydomonas swimming, etc. andthe current progress and future directions of our work.

Xingzhou YangTulane Universityxyang4@tulane.edu

Lisa J. FauciTulane UniversityDepartment of Mathematicsljf@math.tulane.edu

Robert H. DillonWashington State UniversityDepartment of Mathematicsdillon@math.wsu.edu

CP3

Unsteady Stagnation-Point Flow with a MagneticField

The unsteady two-dimensional stagnation-point flow of aviscous fluid impinging on an infinite plate in the pres-ence of a transverse magnetic field is studied. The plateis making harmonic oscillations in its own plane. A finite

difference technique is employed and solutions for large fre-quencies of the oscillations are obtained for various valuesof the Hartmans number.

Fotini LabropuluLuther College - university of Reginafotini.labropulu@uregina.ca

CP3

Performance of Amg-Type Preconditioners forFully-Coupled Solution of Fe Transport/ReactionSimulations

This talk will present recent results of the application ofNewton-Krylov methods with coupled preconditioners thatutilize algebraic multilevel methods. The precondition-ers are evaluated for two different transport/reaction sys-tems: the Navier-Stokes equations for incompressible flowwith transport and reaction, and the solution of the drift-diffusion equations to model semiconductor devices. Per-formance and scaling results for large-scale simulations willbe presented. Sandia is a multiprogram laboratory oper-ated by Sandia Corporation, a Lockheed Martin Company,for the United States Department of Energy’s National Nu-clear Security Administration under contract DE-AC04-94AL85000.

Ray S. TuminaroSandia National LaboratoriesComputational Mathematics and Algorithmsrstumin@sandia.gov

Paul LinSandia National Laboratoriesptlin@sandia.gov

John ShadidSandia National LaboratoriesAlbuquerque, NMjnshadi@sandia.gov

Marzio SalaETHZ Computational Laboratorymarzio@inf.ethz.ch

CP3

Parallel Implicit Adaptive Mesh Refinement forResistive Magnetohydrodynamics

Application of parallel implicit adaptive mesh refinement(AMR) to simulate resistive magnetohydrodynamics is de-scribed. Solving this challenging multi-scale, multi-physicsproblem can improve understanding of reconnection inmagnetically-confined plasmas. Implicit time integrationis used to step over fast Alfven time scales. At each timestep, large-scale systems of nonlinear equations are solvedusing Jacobian-free Newton-Krylov methods together witha physics-based preconditioner on AMR grids.

Michael PerniceLANLpernice@lanl.gov

Luis ChaconLos Alamos National Laboratorychacon@lanl.gov

Bobby Philip

68 CS07 Abstracts

LANLbphilip@lanl.gov

CP4

Is it Possible to Decrease the CFL-Number Depen-dency of Explicit Schemes?

In order to achieve an efficient discretization for LES andDNS of wall-bounded turbulent flows, we are trying to in-crease the stability region of one-stage explicit schemes be-cause a one-stage explicit algorithm is considerably moreefficient and easier to implement than the correspondingmulti-stage scheme. First, we mathematically prove thatit is possible to decrease the CFL-dependency of explicitschemes though at the first glance, it may be inferredthat our conclusion is in contrast with von Neumann the-orem! Then we propose a systematic procedure for sta-bilizing explicit schemes for larger CFL numbers. Themethod is based on tuning the coefficients of higher-orderterms while preserving the consistency of discretization bymatching the coefficients of lower-order terms. Finally,we drive several high-order CFL-independent one-stage ex-plicit schemes. Preliminary results reveal that the currenthigh-order schemes are efficient and bring higher rates ofconvergence.

Arash GhasemiSharif University of TechnologyAzadi Ave., Tehran, Iran, P.O Box : 11365 - 8639ghasemi.arash@gmail.com

CP4

Ripple: Residual Initiated Polynomial-Time Piece-wise Linear Estimation

Piecewise linear estimation algorithms are used in engineer-ing problems, where the individual response functions canbe approximated by linear local approximations. The per-formance of most robust estimation algorithms degradesin higher dimensions due to exponential complexity andsparse data. A robust polynomial-time piecewise linearestimation algorithm has been developed that selects min-imal sets of data based on a minimal residual criterion.RIPPLE is shown to perform better than other robust es-timation algorithms in high dimensions.

Manjula A. IyerVirginia Polytechnic Institute and State Universitymanjula@vt.edu

Layne T. WatsonVirginia Polytechnic Institute and State UniversityDepartments of Computer Science and Mathematicsltw@cs.vt.edu

CP4

Applications of New Matrix Formalism for SeriesSolutions to Some Physical Models

New matrix formalism for finding series solutions to differ-ential equations is presented. The method allows to easilyderive recurrence relations for Laurent coefficients of solu-tions to ODEs and PDEs from a broad class. In particular,the class includes nonnpolynomial ODEs with nonlinearterm in the form f(u(t)) where f is an analytic function.We focus on applications of the method to various modelsin physics including integrable (Burgers, KdV) and nonin-

tegrable (Kuramoto-Sivashinsky, Henon-Heiles) equations.

Sergei UrazhdinWVUsergei.urazhdin@mail.wsu.edu

Lydia S. NovozhilovaWestern Connecticut State Universitynovozhiloval@wcsu.edu

CP5

Complex Version of High Performance ComputingLinpack Benchmark (hpl)

The High Performance Linpack (HPL) Benchmark is usedin benchmarking the TOP 500 computers by solving adense double precision linear system using LU factoriza-tion. HPL can be tuned to use recursive and hybrid algo-rithms and is more efficient than ScaLAPACK PZGESVthat uses only a right-looking algorithm. This effort usesscripts and the C99 compiler to generate a complex versionof HPL to ultimately improve the performance of solversin fusion applications.

Eduardo F. D’AzevedoOak Ridge National LaboratoryMathematical Sciences Sectione6d@ornl.gov

Tony ChanDepartment of MathematicsChinese University of Hong Kongchanhofai@gmail.com

Raymond WongDepartment of MathematicsChinese University of Hong Kongs047815@mailserv.cuhk.edu.hk

Kwai L. WongJoint Institute for Computational ScienceUniversity of Tennessee/ORNLwong@jics.utk.edu

CP5

A New Scaling Formula for the Linpack Benchmark

Dimensional analysis predicts a simple scaling formula forthe Linpack benchmark. The computational power r(p, q),on a set of processors decomposed into a (p, q) grid, is de-termined by the computational power r(p0, q0), on a set ofprocessors decomposed into a (p0, q0) grid, and two scalingparameters α and β such that

r(p, q) = (p/p0)α(q/q0)

βr(p0, q0).

These scaling parameters describe the interaction betweenthe numerical algorithm and the system architetcure. Per-fect scaling corresponds to α = β = 1; no scaling corre-sponds to α = β = 0. The scaling parameters measure thesymmetry of the machine with respect to the chosen algo-rithm and processor decomposition. We have determinedthese parameters by performing a sequence of fixed-timemeasurements where the problem size increases with thenumber of processors such that the execution time remainsconstant. Measurements on a collection of machines con-firm that the conjecture implied by dimensional analysis is

CS07 Abstracts 69

in fact correct.

Robert NumrichUniversity of Minnesotarwn@msi.umn.edu

CP6

Preconditioning the MLFMA Solution of EFIEwith Nested Flexible Iterative Solvers

We consider ill-conditioned dense linear systems generatedby the electric-field integral equation (EFIE) of compu-tational electromagnetics. When such systems are solvedwith the multilevel fast multipole algorithm (MLFMA)within an iterative solver, strong preconditioners areneeded. For this purpose, another (inner) iterative solverthat is nested inside the main (outer) iterative solver canbe used as a preconditioner, provided that a flexible outersolver is used, allowing the preconditioner change from iter-ation to iteration. With this mechanism, the outer solveris used to solve the EFIE system and the inner solver isused to provide the preconditioner. One of the possibilitiesfor the outer solver is the flexible GMRES (FGMRES).

Ozgur Ergul, Tahir Malas, Levent GurelBilkent University, Ankara, TurkeyDept. of Electrical and Electronics Engineeringergul@ee.bilkent.edu.tr, tmalas@ee.bilkent.edu.tr,lgurel@bilkent.edu.tr

CP6

A Parallel Implicit Overlap Method for Solving 3DElectromagnetic Wave Scattering Problems

Maxwells curl equations in the time domain are solvedby combining linear finite element algorithm and the wellknown finite difference time domain method. Hybridmeshes are employed while a local implicit scheme is ap-plied on those tetrahedral elements with tiny grid sizes.Boundary integral term is investigated at PEC boundaries.The complete solution procedure is parallelized. Examplesare included to demonstrate the numerical performance ofthe techniques that are proposed.

Nigel WeatherillUniversity of Wales Swansea, UKCivil and Engineering Computation Centern.p.weatherill@swansea.ac.uk

Zhongqiang XieUniversity of Wales Swansea, UKz.q.xie@swansea.ac.uk

Oubay Hassan, Ken morganUniversity of Walse SwanseaUKo.hassan@swansea.ac.uk, k.morgan@swansea.ac.uk

CP6

Parallelization of Beam Dynamic Code TRACK

In the accelerator design and beam dynamic simulations,it is very important to simulate large number of particles.Parallel computing has been applied to beam dynamic codeTRACK. The space charge effect is described by the Pois-son equation. In this talk we compares several differentparallel models for Poisson equation and give results in theaccelerator simulations. These results show that parallel

computing has greatly improved the capability of acceler-ator design and beam dynamic simulations.

Jin XuPhysics DivisionArgonne National Lab.jin xu@anl.gov

CP7

Scalable Lasto for Electronic-Structure Calcula-tions

We are developing the Scalable Linear Augmented SlaterType Orbital (LASTO) method for electronic-structurecalculations of clusters. To solve Schrodinger equation,we use mixed basis sets which are consisted by a linearcombination of numerical functions inside atom centeredspheres and exponentially decaying functions (Slater-typeorbital, STO) between spheres. As numerical experiments,we compute the Pd clusters and hydrogen absorption of Pdcluster.

Kab Seok KangBrookhaven National LaboratoryComuptational Science Centerkskang@bnl.gov

James DavenportBrookhaven National LaboratoryComputational Science Centerjdaven@bnl.gov

David KeyesColumbia UniversityBrookhaven National Laboratorykd2112@columbia.edu

James GlimmStony Brook UniversityBrookhaven National Laboratoryglimm@bnl.gov

CP8

Computational Issues in Simulation of Gas PipelineNetworks

We are interested in computational issues arising in thecontext of gas flow in pipeline networks. Here, the dy-namics of the flow inside the gas pipes is described by theisothermal Euler equations. In areas of the network wherewe expect less complex gas dynamics, we apply simplifiedmodels for predicting the flow. We discuss algorithms forthe arising coupled hierarchy of gas models and presentnumerical results for a network similar to the CanadianMainline Gas Network.

Michael HertyTechnische Universitaet KaiserslauternFachbereich Mathematikherty@mathematik.uni-kl.de

CP8

Long Memory Mori-Zwanzig Models for the EulerEquations

A long memory model for dimensional reduction, knownas the t-model, is derived through the Mori-Zwanzig for-malism of irreversible statistical mechanics. The model is

70 CS07 Abstracts

applied to the estimation of the rate of decay of solutionsof the Burgers equation and of the Euler equations in twoand three space dimensions. In the Burgers case, the modelcaptures the rate of decay exactly. For the Euler equationsin two space dimensions, the model preserves energy as itshould. In three dimensions, we find a power law decay intime and observe a temporal intermittency. If time per-mits, we will discuss briefly a hierarchy of Mori-Zwanzigmodels in which the t-model is the first one. This is jointwork with A. Chorin, O. Hald and Y. Shvets.

Panagiotis StinisLawrence Berkeley Laboratorystinis@math.lbl.gov

CP8

Identification of Effects of Interface Imperfectionson Turbulent Fluid Flows

We address the problem of characterization of the effectsof initial interface disturbances on a Rayleigh-Taylor flow.The connection between the initial imperfections and theturbulent flow is uncertain and fundamentally nonlinear.To identify the components of the imperfection field thathave the greatest influence on the growth rate, we constructthe Hessian matrix of the transfer function from DNS sim-ulations, and compute the dominant eigenvectors via anadjoint-based matrix-free truncated Lanczos procedure.

Omar Ghattas, Robert Moser, Shan YangUniversity of Texas at Austinomar@ices.utexas.edu, rmoser@ices.utexas.edu,syang@ices.utexas.edu

CP9

A Multiscale Total Variation Based Image Regis-tration Method with Application to Brain Images

Recent studies in total variation models for image restora-tion have led to increased theoretical understanding andpractical implementations of scale space methods for de-composing an image into its essential (cartoon) and spu-rious (noise and texture) parts. Noise and texture add ir-relevant complexity to the data resulting in problems withunnecessary high dimensionality and consequently longerprocessing times. Image registration benefits from such de-composition methods for the essential features detectablein the cartoon image will almost exclusively drive a success-ful registration. We present an image registration methodcombining total variation based image decomposition witha multiresolution triangulation scheme that significantlyreduces problem dimensionality to a few pixels. We demon-strate our method in brain images composed of small andlarge scale structures.

Arthur TogaUCLALaboratory of Neuro Imagingtoga@loni.ucla.edu

Alexandre CunhaCenter for Computational BiologyUniversity of California, Los Angelescunha@ucla.edu

CP9

Variational Shape Optimization for Simultaneous

Segmentation and Denoising of Images

We introduce a novel computational method for theMumford-Shah problem. We recover region boundaries in agiven image and a piecewise smooth approximation. Cast-ing this as a shape optimization problem, we adopt an inex-act Newton approach and propose a finite element methodfor curve evolution. The method incorporates topologicalchanges such as splitting for detection of multiple objects.We employ space adaptivity and a coarse-to-fine approachto process large images efficiently.

Gunay DoganDepartment of Computer and Information ScienceUniversity of Pennsylvaniagdogan@seas.upenn.edu

Ricardo NochettoDepartment of MathematicsUniversity of Maryland, College Parkrhn@math.umd.edu

Pedro MorinDepartamento de MatematicaUniversidad Nacional del Litoral, Argentianpmorin@math.unl.edu.ar

CP9

Regularized 3-D Reconstructions from Spherically-Averaged Fourier Transform Magnitude and Solu-tion X-Ray Scattering Experiments

Measuring the scattering of a beam of x-rays off a solu-tion of identical particles gives data that is the spherically-averaged magnitude of the Fourier transform of electronnumber density in the particle. Since solving a nonlinearleast squares problem does not incorporate all biologicalknowledge about the particles, regularizers are proposedbased on the spherically averaged electron scattering den-sity autocorrelation and based on 2-D and 3-D measures ofcurvature of the particles.

Peter DoerschukCornell Universitypd83@cornell.edu

Youngha HwangPurdue UniversitySchool of Electrical and Computer Engineeringhwangyo@ecn.purdue.edu

CP10

A Boundary Integral Method and AdaptiveTreecode for Poisson-Boltzmann Equation

A boundary integral method (BIM) is developed for com-puting the Poisson-Boltzmann equation (PBE), which isderived from a continuum model of the solvent and coun-terion environment surrounding a biomolecule. The BIMprovides a rigorous treatment on issues of the singu-lar charges, the solute-solvent interfaces, and the infinitedomain associated with the PBE. The boundary inte-grals with regularized kernels are evaluated by an adap-tive treecode algorithm based on Taylor approximationin Cartesian coordinates, and the necessary Taylor coef-ficients are computed by a recurrence relation. Numericalexperiments are included to show the efficiency of the pro-

CS07 Abstracts 71

posed method.

Robert KrasnyUniversity of MichiganDepartment of Mathematicskrasny@umich.edu

Peijun LiDepartment of MathematicsUniversity of Michiganlipeijun@umich.edu

CP10

A Local Regularization Method for the Solution ofFredholm Integral Equation of the First Kind

The solution of many engineering problems involves thesolution of Fredholm integral equation of the first kind

1∫

0

K(s, t)x(t)dt = d(s) , 0 ≤ s ≤ 1

The computational approach to the solution of this equa-tion requires its discretization, which leads to a linear sys-tem of equations of

Kx + e = d

Since the Fredholm integral equation is ill-posed, this lin-ear system is ill-conditioned . For its solution, we use alocal regularization method, as opposed to classical reg-ularization methods, resulting in better approximation ofthe exact solution.

Kourosh ModarresiStanford UniversitySCCMkourosh.modarresi@stanford.edu

Gene GolubStanfordgolub@stanford.edu

CP10

Numerical Analysis of An Integro-DifferentialEquation

Consider the integro-differential equation

ut(x, t) = ε

∫Ω

J(x− y) (u(y, t) − u(x, t)) dy + f(u),

with initial condition u(x, t0) = u0(x), x ∈ Ω, t > 0, Ω ⊆Rd with d = {1, 2, 3} , ε > 0, J(x) = J(−x) and f(u) is abistable function. This type of initial value problem (IVP)arises in the modelling of various physical and biologicalprocess. We study the numerical analysis of this IVP andalso investigate its long time dynamics.

Bhowmik K. SamirPostgraduate research studentDept. of Mathematics, Heriot Watt Universitys.k.bhowmik@ma.hw.ac.uk

CP11

A Level Set Approach to Dislocation Models ofLow-Angle Grain Boundary Structure and Motion

Dislocation models are useful for gaining insight into the

meso-scale structure and motion of low-angle grain bound-aries. Using a level-set formalism for dislocation dynamicspioneered by our group, we examine the equilibrium struc-ture of grain boundaries formed from straight-line disloca-tion networks constructed using Frank’s formulas. We alsoinvestigate the dependence of grain boundary mobility onthe mobility of individual dislocations and grain boundarygeometry. The computational efficiency required to studythese models is provided by a parallel level set method soft-ware library (LSMLIB) that we have recently developed.

Kevin T. Chu, Adele Lim, David SrolovitzMechanical & Aerospace EngineeringPrinceton Universityktchu@princeton.edu, atlim@princeton.edu, srol@yu.edu

Yang XiangDepartment of MathematicsHKUSTmaxiang@ust.hk

CP11

High-Order Mimetic Finite-Difference Modeling ofShear Crack Propagation

A fourth-order finite-difference traction-at-split-node im-plementation of faulting boundary conditions is presentedin this work. Geometry of the fault and initial shear stressallow only in-plane motion which is modeled in the plane(x,z). Our two dimensional method combines a one-sideddiscretization of the jump conditions along the fault seg-ment with a staggered discretization of the equations ofmotion within interior of the embedding medium. Fourth-order numerical differentiation of elastic fields is performedin the whole domain by using a new set of differentiatorscalled mimetic or conservative finite differences. Conver-gence and accuracy of our algorithm are shown through twotest cases. First, the analytical solution of a self-similarfixed-rupture velocity model is reproduced as the grid sizedecreases. Next, we simulate the propagation of a sponta-neous rupture, governed by a linear slip-weakening frictionlaw that defines a cohesive law. Our results are assessedusing an alternative numerical solution given by a well es-tablished Dynamic Fault Model (DFM) algorithm.

Otilio RojasComputational Science Research CenterSan Diego State Universityrojas@sciences.sdsu.edu

CP11

Morphology of Critical Nuclei in Solid State PhaseTransformations

Predicting the shape of a critical nucleus in solids has beena long-standing problem in solid-state phase transforma-tions. We present a diffuse-interface approach togetherwith minimax algorithm for predicting the critical nucleusmorphology in elastically anisotropic solids. It is foundthat strong elastic interactions may lead to critical nucleiwith non-convex shapes.

Lei ZhangDepartment of MathematicsPenn State Universityzhang l@math.psu.edu

Qiang DuPenn State University

72 CS07 Abstracts

Department of Mathematicsqdu@math.psu.edu

CP12

Hessian-Based Model Reduction forPDE-Constrained Optimization

We present a new methodology to create reduced-ordermodels for large-scale, ill-posed inverse problems. Theproblem of determining a suitable reduced basis is for-mulated as a sequence of optimization problems. Weshow that, under certain non-restrictive assumptions, theseproblems have a closed-form solution that entails compu-tation of the dominant eigenvectors of a Hessian matrix.Furthermore, the method scales well to problems with alarge number of parameter inputs. The methodology isdemonstrated for a large-scale contaminant transport in-verse problem.

Karen E. WillcoxMITkwillcox@MIT.EDU

Omar GhattasUniversity of Texas at Austinomar@ices.utexas.edu

Bart G. Van Bloemen Waanders, Judith HillSandia National Laboratoriesbartv@sandia.gov, jhill@sandia.gov

Omar BashirMITbashir@mit.edu

CP12

A Two-Dimensional Arnoldi Algorithm for ModelOrder Reduction of Parameterized Linear Dynam-ical Systems

The presence of parameters and variability in the de-sign and manufacturing process of modern microelectron-ics poses new challenges to existing model reduction tech-niques. In this talk, we present a multiparameter moment-matching reduction algorithm for the simulation and anal-ysis of large scale parametrized linear dynamical systems.The new algorithm uses a novel two-dimensional Arnoldiprocess and is computationally stable and robust. In ad-dition, it is structural preserving. Examples from pa-rameterized integrated circuits and microelectromechanical(MEMS) devices will be used to compare the new algorithmwith the existing ones.

Yangfeng SuDepartment of MathematicsFudan University, Chinayfsu@fudan.edu.cn

Zhaojun BaiUniversity of Californiabai@cs.ucdavis.edu

Yung-Ta LiDept. of MathematicsUC Davisytli@math.ucdavis.edu

Xuan Zeng

ASIC & System State Key Lab.,Microelectronics Dept., Fudan Universityxzeng@fudan.edu.cn

CP12

Reduced System Computing for Singularly Per-turbed Differential Equations

Reduced System Computing (RSC) is a software systemfor studying singularly perturbed differential equations. Itavoids the problem of numerical stiffness by concatenat-ing solutions to the fast and slow subsystems that arise inthe singular limits of the differential equations. Tools forsolving initial value problems and for computing periodicorbits will be presented, along with an application of RSCto a pair of coupled relaxation oscillators.

Warren WeckesserColgate UniversityDepartment of MathematicsWWeckesser@mail.colgate.edu

CP13

Direct Linear Solvers for Finite Element Modellingof Large Industrial Applications

Krylov subspace methods are widely used in simulationsoftwares even if they are all likely to suffer from slowconvergence and divergence for problems which arise fromlarge industrial applications. The main reason for this isthat direct solvers based on matrix factorization are verymemory consuming methods which may be unfeasible onlarge problems. We will discuss here the possibility of an ef-ficient direct solving of large problems discretized by meansof finite elements.

Isabelle CharpentierInstitut d’Informatique et Mathematiques AppliqueesIsabelle.Charpentier@imag.fr

Cedric DoucetLaboratoire de Modelisation et Calcul (IMAG)Grenoble - Francecedric.doucet@cedrat.com

CP13

Sparse Direct Factorizations Based on Unassem-bled Hyper-Matrices

For dynamic FEM applications, existing sparse directsolvers can be said to solve the wrong problem. They op-timize the solution of a single linear system, while the realproblem is to solve a series of systems that are derived fromgradual h/p refinement of a FEM discretization. We showhow a combination of elementary concepts gives a solverthat is space and time efficient, and that is eminently suitedto the dynamic case.

Paolo BientinesiDepartment of Computer SciencesThe University of Texas at Austinpauldj@cs.utexas.edu

Robert A. van de GeijnThe University of Texas at AustinDepartment of Computer Sciencervdg@cs.utexas.edu

CS07 Abstracts 73

Victor EijkhoutThe University of Texas at AustinTexas Advanced Computing Centereijkhout@tacc.utexas.edu

Jason KurtzInstitute for Computational Engineering and SciencesThe University of Texas at Austinkurtzj@ices.utexas.edu

CP13

Combinatorial Preconditioners for Scalar EllipticFinite-Elements Problems

The talk will present a new preconditioner for linear sys-tems arising from finite-elements discretizations of scalarelliptic PDE’s. The algebraic equations that we solve areKx = b, where K =

∑eKe is a sum of element matri-

ces Ke. The solver splits the collection {Ke} of elementmatrices into a subset of matrices that are approximableby diagonally-dominant matrices and a subset of matricesthat are not approximable. The approximable Ke’s are ap-proximated by diagonally-dominant matrices Le that arescaled and assembled to form a global diagonally-dominantmatrix L. A combinatorial graph algorithm approximatesL by another diagonally-dominant matrix M that is mucheasier to factor. The inapproximable element matrices areadded to M and the sum is factored and used as a precon-ditioner. When all the element matrices are approximable(in particular, when they are all well-conditioned), which isoften the case, the preconditioner is provably efficient. Ex-perimental results show that on some problems, especiallyproblems with some ill conditioned elements, the precondi-tioner is more effective than an algebraic multigrid solverand than an incomplete-factorization preconditioner.

Gil ShklarskiSchool of Computer ScienceTel-Aviv Universityshagil@tau.ac.il

Haim AvronTel Aviv Universityhaima@tau.ac.il

Sivan A. ToledoTel Aviv UniversitySchool of Computer Sciencestoledo@tau.ac.il

CP14

Scalable Metadata and Algorithms for StructuredAMR

Metadata for structured adaptive mesh refinement(SAMR) contains information about the grids forming themesh. It grows with the number of grids. In parallel, wherethe global number of grids grows with the number of pro-cessors, metadata grows rapidly, leading to severe ineffi-ciencies starting around 1K processors. We present new al-gorithms for managing SAMR meshes without global meta-data. Significant parallel efficiency is obtained through nothaving to generate or operate on the global metadata.

Brian GunneyLawrence Livermore National Labgunney1@llnl.gov

CP14

An Efficient Linearity-and-Bound-Preserving Con-servative Interpolation (Remapping) Method forMeshes with Changing Connectivity

Remapping is one of the essential parts of most ArbitraryLagrangian-Eulerian (ALE) methods. In this talk, we ex-tend the idea of swept integration method to the grids withchanging connectivity during the smoothing stage. We fo-cus to the Voronoi meshes in 2D, which are used for realnumerical simulations. We present several numerical exam-ples to show that properties of this algorithm (conservativ-ity, linearity and bound preservation) remain unchangedfor grids with different topology.

Mikhail ShashkovLos Alamos National Laboratoryshashkov@lanl.gov

Milan KucharikLos Alamos National Labkucharik@lanl.gov

CP14

Multi-Material Interface Reconstruction UsingParticles and Power Diagrams

We present a new method for interface reconstructionin multi-material flow simulations. The method intro-duces particles into mixed cells and uses an an attraction-repulsion model to draw particles of the same material typetogether. The interface is then reconstructed from the par-ticles using a weighted Voronoi diagram or Power Diagram.The new method eliminates the material order dependenceof the interface topology commonly seen in VOF recon-struction of three or more materials in a cell.

Samuel P. Schofield, Raphael Loubere, Rao V. Garimella,Marianne FrancoisLos Alamos National Laboratorysams@lanl.gov, loubere@lanl.gov, rao@lanl.gov, mm-fran@lanl.gov

CP15

Desensitization and the Ignition-And-GrowthModel

Of the various macro-scale continuum models of reac-tive flow in high-energy explosives, the ignition-and-growthmodel has been the most widely used. Well-resolved com-putational experiments with the model demonstrate thatit does not explicitly account for the desensitization of het-erogeneous explosives, caused by exposure to low strengthshocks. A modification to the model that accounts for thedesensitization process is proposed. Numerical simulationsemploying adaptive mesh refinement on composite overlap-ping grids with the augmented model are conducted.

Guilherme De OliveiraWorcester Polytechnic InstituteVisiting Assistant Professorgdo@wpi.edu

CP15

Laser Generated Elastic Waves in a Semi-InfiniteSolid

Analytical and numerical issues for thermoelastic waves by

74 CS07 Abstracts

a pulsed laser in a semi-inifinite solid were investigated.Analytic solutions were derived by using Laplace Trans-form techniques for thermal and mechanical problems. Theeffect of optical absortion coefficients on the thermal anddisplacement fields was studied. All numerical results werecompared with the analytic solutions.

Bongsoo JangDept of MathematicsKent State University at Ashtabulabjang1@kent.edu

Harish CherukuriDepartment of Mechanical Engineering and EngineeringScienceUniversity of North Carolina at Charlottehcheruku@uncc.edu

CP15

Operator Splitting and Acceleration Methods forSolving the Neutron Transport Equation in 1-DSpherical Geometry

Our study concerns the iterative resolution of the neutrontransport equation in 1-D spherical geometry. More pre-cisely, we consider a splitting method for the collision op-erator taking into account the caracteristics of the trans-port operator. An infinite dimensional adaptation of SORalgorithm and Splitting-Diffusion Synthetic Acceleration(DSA) method are used to accelerate the procedure. Theo-retical aspect for these methods are discussed, and numer-ical results are presented.

Abdelkader TizaouiUniversite Paul SabatierMIP (Mathematiques pour l’Industrie et de la Physiqueabdelkader.tizaoui@iut-tlse3.fr

CP16

Computable Condition Number Estimates forLarge Least Squares Problems

Some parameter estimation problems lead to huge denseleast squares problems that require a good knowledge ofthe problem conditioning. We propose computable statis-tical estimates for the conditioning of a linear function ofthe least squares solution. We present the correspondingparallel implementation in the framework of space geodesyand we study how these quantities compare with availableestimates for large number of unknowns. The issues of rankdeficient least squares problems are also addressed.

Marc BaboulinCERFACSbaboulin@cerfacs.fr

CP16

A Comparison of Two Algorithms for Predictingthe Condition Number

We present experimental results of comparing the ModifiedK-Nearest Neighbor (MkNN) algorithm with Support Vec-tor Machine (SVM) in the prediction of condition numbers.While SVM is considered a state-of-the-art classification/regression algorithm, kNN is usually used for collaborativefiltering tasks. Since prediction can also be interpretedas a classsification/regression task, virtually any super-vised learning algorithm (such as kNN) can also be ap-

plied. Experiments were performed on one publicly avail-able dataset. We conclude that Modified kNN (MkNN)performs much better than SVM on this particular dataset.

Dianwei HanComputer science department,University of Kentuckydianweih@csr.uky.edu

Jun ZhangUniversity of KentuckyDepartment of Computer Sciencejzhang@cs.uky.edu

CP17

Finite Difference Techniques For Delay DifferentialProblems With Layer Behavior

This study deals with the singularly perturbed initial valueproblems for linear and quasilinear delay differential equa-tions. The numerical methods are generated on a gridthat is constructed adaptively from a knowledge of the ex-act solution, which involve appropriate piecewise-uniformmeshes on each time subinterval. An error analysis showsthat the discrete solutions are uniformly convergent withrespect to the perturbation parameter. The parameter uni-form convergence is confirmed by numerical computations.

Ilhame AmiraliyevaYuzuncu Yil University,Faculty of Agricultureilhame@yyu.edu.tr

Gabil AmiraliYuzuncu Yil University, Faculty of Art and Sciences,Department of Mathematicsgamirali2000@yahoo.com

CP17

Higher Order Finite Difference Methods for Sec-ond Order Singularly Perturbed Delay DifferentialEquations

The approximation of solutions Delay differential equa-tions(DDEs) has been a problem of great importance dueto the versatility of its application in various fields. De-velopment of numerical methods for DDEs are challengingbecause we have to use an appropriate approximation for

the retarted arguments like u(x ± δ) and u′(x − δ) and

the algorithm has to take care of the jump discontinuiesdue to the delay/advance. We will discuss a few higherorder finite difference methods for second order singularlyperturbed differential equation with delay/advance and itscomputational complexity.

V.P. RameshIndian Institute of Technology Kanpur(Student)vpramesh@iitk.ac.in

Mohan KadalbajooIndian Institute of Technology KanpurKanpur Indiakadal@iitk.ac.in

CP18

Sparse Computation on a P2P System

We present the 2-degree polynomial (2DP) A(Ax+x)+x

CS07 Abstracts 75

distribution on a peer-to-peer system, where A is a largesparse matrix. Such 2DP represents the kernel of manyiterative methods for solving sparse linear algebra prob-lems. We propose a distribution technique based on datafragmentation engendering a good communication patternand show that our solutions need a pre-processing for ma-trix fragmentation by solving an NP-Complete problem butguarantee load balance.

Olfa Hamdi-LarbiUniversity of Versailles, PRiSM Laboratory, Franceolfa.hamdi@ensi.rnu.tn

Zaher MahjoubFaculty of Sciences of Tunis, Tunsiazaher.mahjoub@fst.rnu.tn

Nahid EmadUniversity of Versailles, PRiSM LaboratoryNahid.Emad@prism.uvsq.fr

CP18

Reshape: A Framework for Dynamic Resizing andScheduling of Homogeneous Applications in a Par-allel Environment

Due to the unpredictability in job arrival times and vary-ing resource requirements, static scheduling results in idlesystem resources, thereby decreasing the overall systemthroughput. To alleviate this drawback, we have devel-oped a framework called ReSHAPE which supports dy-namic resizing of parallel MPI applications executed ona distributed memory architecture. Our presentation de-scribes the ReSHAPE framework architecture and presentsresults from testing the framework with structured appli-cations that have two-dimensional data arrays distributedacross a two-dimensional processor grid.

Rajesh SudarsanDepartment of Computer Science, Virginia Techsudarsar@vt.edu

Calvin J. RibbensVirginia TechDepartment of Computer Scienceribbens@vt.edu

CP18

Dynamic Load Balancing for Hyperthreaded andMulti-Core Cluster Nodes

There has been a significant shift by processor manufac-turers from increasing clock speeds to on-chip parallelism:hyperthreaded and multi-core chips. These processors arebecoming common in desktop systems and cluster nodes,but it is not clear how to use them most efficiently. Thistalk will give a brief overview of the technology and reportexperiences using the DRUM resource aware dynamic loadbalancing system in cluster environments that include dualcore and hyperthreaded processors.

James D. TerescoDepartment of Computer ScienceWilliams Collegeterescoj@cs.williams.edu

CP19

Multiscale Simulation of Ionic Flux Through a

Nanopore Under Applied Electric Potential

We present a multiscale model to simulate ionic fluxthrough a nanopore of an electrodesalination membrane.The model relies on Brownian Dynamics simulations in-side the nanopore, coupled with a Poisson-Nernst-Planckcontinuum model in the pore vicinity. The model is val-idated against measurements of current through track-etched nanoporous membranes under an applied electricpotential. Simulations are performed to investigate the ef-fects of pore size, membrane charge and applied potentialon throughput and selectivity.

Habib N. NajmSandia National LaboratoriesLivermore, CA, USAhnnajm@sandia.gov

Kevin LongSandia National Laboratorieskrlong@sandia.gov

Blake SimmonsNanoscale Science & TechnologySandia National Laboratories, Livermore CAbasimmo@sandia.gov

Bert J. DebusschereDepartment of Biological and Energy SciencesSandia National Laboratories, Livermore CAbjdebus@sandia.gov

Michael HicknerSandia National LaboratoriesAlbuquerque, NMmahickn@sandia.gov

Pierre PonceSandia National LaboratoriesLivermore, CApponce@sandia.gov

Helgi AdalsteinssonSandia National Laboratories, Livermore CAhadalst@sandia.gov

CP19

Mathematical Modeling and Simulation of TextureEvolution

Preparing a texture suitable for a given purpose is a centralproblem in materials science, which presents many chal-lenges for mathematical modeling, simulation, and anal-ysis. We focus on the mesoscopic behavior of the grainboundary system and on understanding the role of topo-logical reconfigurations during evolution. We formulateseveral types of evolution equations based on fractional ki-netics and stochastic descriptions, compare its results withthe simulations and discuss their limitations and possibleextensions to higher dimensions.

Maria EmelianenkoDept. of Mathematical SciencesCarnegie Mellon Universitymasha@cmu.edu

Dmitry GolovatyThe University of AkronDepartment of Theoretical and Applied Mathematics

76 CS07 Abstracts

dmitry@math.uakron.edu

Shlomo Ta’asanDepartment of Mathematical SciencesCarnegie Mellon Universityshlomo@andrew.cmu.edu

David KinderlehrerCarnegie Mellon Universitydavidk@andrew.cmu.edu

CP19

Mesoscopic Simulation of Self-Organization in Sur-face Processes

The self-organization of constituents in a two phase mix-ture through diffusion is known as Ostwald ripening. Thismultiscale phenomenon can be modeled using a class ofmesoscopic models consisting of stochastic partial differen-tial equations. In this talk, spectral schemes for stochas-tic partial differential equations are described and conver-gence verified using exactly solvable benchmark problems.These schemes are then applied to the mesoscopic modeland the simulation results are compared with theoreticalresults such as the Lifshitz-Slyozov growth law; long timeresults are also described.

David J. HorntropDepartment of Mathematical SciencesNew Jersey Institute of Technologydavid.horntrop@njit.edu

CP20

Title: On Multi-Phase Flows

In this lecture, we will discuss some of the issues relatedto stability of flows involving multiple interfaces and com-puting of such flows efficiently. Results will be presented.This is an ongoing work.

Prabir DaripaTexas A&M UniversityDepartment of Mathematicsprabir.daripa@math.tamu.edu

CP20

Compressible Multispecies Multiphase Flow Mod-els

We develop comopressible multispecies multiphase flowmodels with surface tension and transport. We proposea closure model which satisfies all the conservation andboundary conditions after averaging the primitive equa-tions of mass, momentum and energy. We derive three in-terfacial exact quantities v∗, p∗, (pv)∗ directly from theseaveraged equations to validate our model with Rayleigh-Taylor instability simulation which have been validatedagainst the real experiment. We also observe other proper-ties of our simulation based on theories and experiments.

Hyunsun LeeSUNY at Stony Brookhslee@ams.sunysb.edu

CP20

A VOF-PLIC Method for Axisymmetric Multi-

phase Flow

A piecewise linear interface calculation in axisymmetric ge-ometries is presented and implemented within RIPPLE, a2D volume-of-fluid code. Analytical relations between theinterface parameters and volume fractions are provided,emphasizing resolution of a numerical instability that oc-curs when one of the components of the normal vector atan interface approaches zero. Results are presented for thecollapse of a cylindrical water column and the wake dy-namics of one or two rising bubbles.

Jie Dai, James SterlingKeck Graduate Institutedwd6810@yahoo.com, jim sterling@kgi.edu

Ali NadimClaremont Graduate UniversityDepartment of Mathematicsali.nadim@cgu.edu

CP21

Least Squares Finite Element Solution for Vis-coelastic Flow Problems

The goal of this work is to implement a least squares finiteelement approach for the equations governing viscoelasticflows such as those occurring in polymer processes. TheOldroyd-B and Giesekus viscoelastic constitutive equationsare considered, as well as Newtonian and non-Newtonian(Carreau model) formulations. The least squares methodoffers the advantage of generating a symmetric positive def-inite system of equations, and has also been recognizedas potentially effective in addressing the high Weissenbergnumber problem which characterizes viscoelastic flows. Wecompare results of the weighted least squares approach tothose using standard Galerkin techniques. An adaptivemesh technique designed for regions of high gradients in2D is also presented.

Christopher L. CoxClemson UniversityDept of Mathematical Sciencesclcox@clemson.edu

Tsu-Fen ChenDepartment of MathematicsNational Chung Cheng Universitytfchen@math.ccu.edu.tw

Sheue Jen LeeNational Chung Cheng UniversityDepartment of Mathematicssheuelee@mail.wtuc.edu.tw

Patti SylviaDepartment of Mathematical SciencesClemson Universityspatti@clemson.edu

CP21

Derivative-Free Approaches for Maximizing theLifetime of a Polymer Extrusion Filter

We consider an extrusion filter used to remove debris froma polymer melt before the liquid is spun into a fiber. Weseek the optimal parameters to maximize the lifetime ofthe filter using a simulator developed at the Center forAdvanced Engineering Fibers and Films (CAEFF). The

CS07 Abstracts 77

simulator must work as a black-box in conjunction with aderivative-free optimization algorithm. We present prelim-inary numerical results obtained with a variety of samplingmethods for optimization.

Brian MccluneClarkson UniversityDepartment of Mathematics and Computer Sciencemcclunbp@clarkson.edu

Lea JenkinsClemson UniversityDepartment of Mathematicslea@clemson.edu

Adam Rose, Kathleen FowlerClarkson Universityroseai@clarkson.edu, kfowler@clarkson.edu

CP21

A Hard Constraint Algorithm to Model ParticleInteractions in Polymeric Flows

We present a new algorithm to model short-range particleinteractions in polymer-laden fluids. In this method thepolymer is represented by a bead-rod model fully-coupledto a Newtonian solvent through hydrodynamic drag andBrownian motion. The central feature is a new rigid con-straint algorithm whereby rods elastically bounce off oneanother to prevent crossing in polymer-polymer interac-tions, similar to our treatment of polymer-surface interac-tions. We apply the method to DNA-laden flows in arraymicrochannels.

David TrebotichLawrence Livermore National Laboratorytrebotich1@llnl.gov

Gregory H. MillerUC Davis & LBNLgrgmiller@ucdavis.edu

CP22

Towards An Accurate Performance Modeling ofParallel Sparse LU Factorization

We present a performance model to analyze a paral-lel sparse LU factorization algorithm on modern cached-based, high-end parallel architectures. Our model char-acterizes the algorithmic behavior by taking account theunderlying processor speed, memory system performance,and the interconnect speed. The model is validated usingthe SuperLU DIST solver, sparse matrices from real appli-cation, and an IBM POWER3 parallel machine. It can beeasily adapted to study performance of other sparse fac-torizations, such as Cholesky or QR.

Laura GrigoriINRIAFrancelaura.grigori@irisa.fr

Xiaoye S. LiComputational Research DivisionLawrence Berkeley National Laboratoryxsli@lbl.gov

CP22

On Reducing Memory Usage of the Simulations Us-ing Sparse Direct Solvers

Simulating LARGE multi-cavity accelerator structureswith the finite element method is limited by availablecomputer memory when the sparse direct solver is usedto solve the resulting linear systems. This talk willpresent various ways of reducing the memory usage ofthe capability-computing simulations that use sparse directsolvers thereby allowing eigenvalue problems consisted ofhundred million DOFs to be solved on existing computingplatforms.

Volkan Akcelik, Ernesto Prudencio, Lixin Ge, Kwok Ko,Lie-Quan LeeStanford Linear Accelerator Centervolkan@slac.stanford.edu, prudenci@slac.stanford.edu,lge@slac.stanford.edu, kwok@slac.stanford.edu,liequan@slac.stanford.edu

CP22

Using Sparse Lu to Compute the Null Space of aRectangular Matrix

Computing the null space of a sparse matrix is an impor-tant component of some computations, such as graph em-beddings and parameterization of mesh data. We proposean efficient and reliable method to compute an orthonor-mal basis of the null space of a sparse square or rectangularmatrix (usually with more rows than columns). The maincomputational component in our method is a sparse LUfactorization with partial pivoting of the input matrix; thisfactorization is significantly cheaper than the QR factor-ization used in previous methods. We analyze importanttheoretical aspects of the new method and demonstrateexperimentally that it is efficient and reliable.

Craig GotsmanCS dept., Technion, Israelgotsman@cs.technion.ac.il

Sivan A. ToledoTel Aviv UniversitySchool of Computer Sciencestoledo@tau.ac.il

CP23

On the Design of Diffusion Constants for RandomWalks of Squares, Triangles and Cubes

I show how to design the value of the diffusion constant Dfor both the random walks of Squares and Triangles overtheir respective regular lattices in two-dimensions, and fora random walk of a Cube on the three-dimensional Carte-sian lattice. By allowing movements to grid locations otherthan nearest neighbors, I can design the value of the diffu-sion constant D to a value other than unity.

J.F. NystromShepherd Universityjnystrom@shepherd.edu

CP23

Bandlimited 1/f Noise: a Signal for Robust Exper-iment Design

Experiment design aims to find a suitable input signal to

78 CS07 Abstracts

maximise the information obtained from an experiment.This input signal typically depends on the actual plant. Toenhance robustness, it is important to use signals which arenear optimal over a range of systems. Here we introduce“bandlimited 1/f noise” as an signal with such a property.We also present a simple and fast algorithm for generatingbinary signals with this spectrum.

Cristian R. Rojas, James S. Welsh, Graham C. GoodwinSchool of Electrical Engineering and Computer ScienceThe University of Newcastle, Australiacristian.rojas@studentmail.newcastle.edu.au,james.welsh@newcastle.edu.au,graham.goodwin@newcastle.edu.au

CP24

Estimation of Blood Alcohol Concentration by In-version of a Diffusion Model

A protocol for estimating blood alcohol concentration isproposed. This methodology requires calibrating short pe-riod data coming from a skin sensor to the subject understudy and then inverting the forward model for long pe-riod data. A simulation study is performed to observe theinfluence of parameter changes on vapor alcohol removedthrough the skin and blood alcohol concentration. Thisavoids calibrating model parameters to subjects to whomit is not ethic to offer alcohol.

Miguel A. DumettUniversity of Southern CaliforniaDepartment of Mathematicsdumett@almaak.usc.edu

CP24

Application of the Stochastic Galerkin Method forAnalysis of Human Cardiac Ion Channel Models

Based on the Weiner-Hermite polynomial chaos expansion,the stochastic Galerkin method efficiently computes nu-merical solutions for stochastic systems. Unlike such tech-niques as sensitivity analysis, perturbation methods, andsecond moment-analysis, this method is applicable to alarge number of systems while requiring less computationaleffort than sampling based stochastic methods like MonteCarlo. We utilize the stochastic Galerkin method to assessthe impact of stochastic rate coefficients on the predictionsof Markovian cardiac ion channel models.

Sarah E. GeneserSchool of Computing, University of Utahgeneser@cs.utah.edu

Mike KirbySchool of Computing,University of Utahkirby@cs.utah.edu

Frank SachseCardiovascular Research and Training Institute,University of Utahfs@cvrti.utah.edu

Dongbin XiuDepartment of MathematicsPurdue Universitydxiu@math.purdue.edu

CP24

A Coupled Diffusion-Elasticity PDE-ConstrainedFramework for Simulating Gliomas Growth: aMedical Imaging Perspective

Primary brain tumors constitute a significant health chal-lenge, due to their grim prognosis. More than 50% of pri-mary brain tumors are gliomas, which are seldom treat-able with resection and ultimately progress to high-grade,leading to death in only 6-12 months. There is a press-ing need for deepening our understanding of the charac-teristics of the spatio-temporal progression of brain can-cer, and for determining predictive factors for cancer inva-sion, using phenotypic cancer profiles derived from imag-ing, histopathology and potential other sources. Such pre-dictive factors would allow us to apply more aggressivetreatments, yet treatments that are spatially adaptive totissue that is highly likely to be invaded by cancer, in orderto maintain patient functioning at acceptable levels. Thiswork proposes a simple unified framework for modelinggliomas growth and the subsequent mechanical impact onthe surrounding brain tissue (mass-effect), with estimationof unknown parameters via a PDE-constrained optimiza-tion method. We target a medical imaging context, wheresuch a framework primarily aims at the following goals: (1)improving the deformable registration from the brain tu-mor patient image to a common stereotactic space (atlas);and (2) having, to a certain extent, predictive capabilitiesfor glioma growth, after its parameters are estimated for agiven patient. The first is important for integrative statis-tical analysis of tumors in groups of patients and surgicalplanning. The second is important for general treatmentplanning and prognosis. To our knowledge, this is amongthe first attempts in the specialty literature to introducea PDE-constrained optimization formulation in the con-text of modeling tumor growth based on available patientimaging data. The present work is dedicated mostly toformulation and methods, with extensive 1D numerical ex-periments performed for a preliminary evaluation of theoverall formulation/methodology. The 3D MRI-based sim-ulations are work-in-progress; a simplified biomechanicalversion has already been implemented and reported else-where.

Cosmina HogeaSection of Biomedical Image Analysis, Dept.University of Pennsylvaniahogeac@uphs.upenn.edu

George BirosUniversity of Pennsylvaniabiros@seas.upenn.edu

Christos DavatzikosSection of Biomedical Image Analysis, Dept. of RadiologyUniversity of Pennsylvaniachristos.davatzikos@uphs.upenn.edu

CP24

Non-Newtonian Blood Flow in a Stenosis andAneurysm: Transient and Steady State Simula-tions.

This study considers the steady state and transient simula-tions of blood flow through two three-dimensional modelsof an arterial stenosis and an abdominal aortic aneurysm.Four non-Newtonian blood models, namely the Power Law, Casson, Carreau and the Generalized Power Law, aswell as the Newtonian model of blood viscosity, are used

CS07 Abstracts 79

to investigate the flow effects induced by these differentblood constitutive equations. Results show significant dif-ferences between modelling blood as a Newtonian and non-Newtonian fluid. The dependence of the flow on the di-mensionless parameters is examined and differences fromthe Newtonian case are discussed.

Chris LangdonLuther CollegeUniversity of Reginaneallanc@uregina.ca

Iqbal HusainLuther College - MathematicsUniversity of ReginaIqbal.Husain@uregina.ca

CP24

Brain Surface Conformal Parameterization withAlgebraic Functions

Here, we introduce a parameterization method for brainsurfaces based on algebraic functions. By solving the Yam-abe equation with the Ricci flow method, we can confor-mally map a brain surface to a multi-hole disk. The result-ing parameterizations do not have any singularities and areintrinsic and stable. It also offers a method to explicitlymatch landmark curves between anatomical surfaces suchas the cortex, and to compute conformal invariants for sta-tistical comparisons of anatomy.

Yalin WangMathematics DepartmentUniversity of California, Los Angelesylwang@math.ucla.edu

Tony F. ChanNational Science Foundationtfchan@nsf.gov

CP25

Accurate High-Performance Multigrid Solvers inReconfigurable Hardware

In this paper, we present a hardware implementation ofthe V-cycle Multigrid method for finding the solution ofa 2D-Poisson equation. We use Handel-C to implementour hardware design, which we map onto available FieldProgrammable Gate Arrays(FPGAs). We analyze the im-plementation performance using the FPGA vendors’ tools.We compare our findings with a C++ version of thr algo-rithm. The obtained results show better performance whencompared to existing software versions.

Safaa J. KasbahLebanese American University, Division of ComputerScienceand Mathematicssafaa.kasbah@lau.edu.lb

Issam DamajDepartment of Electrical and Computer EngineeringDhofar Universityi damaj@du.edu.om

Ramzi HaratyLebanese American University, Division of ComputerScienceand Mathematics

rharaty@lau.edu.lb

CP25

Inverse Molecular Design by Local Enumeration

In previous work we have developed a method for the in-verse design of chemical structures (Chuchwell et al., 2004;Brown et al., 2006). A key step in our method involvesthe solution of a system of constrained linear Diophantineequations. In this work we describe a novel method for thesolution of these equations using the Fincke-Pohst algo-rithm. This approach simultaneously controls both combi-natorial explosion and extrapolation error. We benchmarkour method against past results.

Shawn MartinComputational Biology Dept.Sandia National Laboratoriessmartin@sandia.gov

William BrownComputational BiologySandia National Laboratorieswmbrown@sandia.gov

CP25

Credibility: How Will Science Judge Our Mathe-matical Or Computerised Models?

We review the literatures of computational languages andsimulation methodology so as to investigate the answer tothe ultimate question asked of any of our mathematical orcomputerised models, particularly those in the life sciences:viz., credibility. We compare and contrast the two model-building activities, reaching thereby an understanding ofthe Scientific Method, itself then revealed to be a quite pre-human process: quite biological (first genes; then neurons),this model-building process has ensured biological survival.

Danielle Mihram, G Arthur MihramUniv of Southern Californiadmihram@usc.edu,

CP25

Formal Constraints on Memory Management inOverloaded Arithmetic

Memory management rules for overloaded arithmetic areexpressed in the Object Constraint Language (OCL) andapplied to an advection/diffusion model. One set of con-straints eliminates memory leaks. A second set ensureseconomical memory recycling. It is demonstrated that run-time assertion checks inspired by the constraints exposedan exceptionally hard-to-reproduce compiler bug. Further-more, the interplay between OCL and Fortran capabilitiesled to a breakthrough that improved the readability of ourcode by facilitating operator overloading.

Xiaofeng XuUniv. of Maryland, College ParkDept. of Fire Protection Engineeringxxf@umd.edu

Karla MorrisGraduate Center of CUNYMechanical Engineering Dept.karla morris@hotmail.com

80 CS07 Abstracts

Damian W. RousonU.S. Naval Research LaboratoryCombustion Modeling & Scalingdamian.rouson@nrl.navy.mil

CP26

Robustness of the Multivariate Spline Method forNumerical Solution of Partial Differential Equa-tions

Multivariate spline functions are smooth piecewise polyno-mial functions over triangulations consisting of n-simplicesin the Euclidean space Rn. We review how they are usedwith Lagrange multipliers to enforce the smoothness con-ditions, the boundary conditions and the constraints in nu-merical solution of partial differential equations. We thendemonstrate the robustness of this approach on two singu-lar perturbation problems, a fourth order problem and aStokes-Darcy flow.

Gerard AwanouNorthern Illinois Universityawanou@math.niu.edu

CP26

Alternative Way to Solve Nonlinear PDEs

Generally Newton-Krylov method is the first choice in solv-ing nonlinear problems. But it is expensive to construct Ja-cobian matrix at each iteration, Even the Jacobian-free oneis used, information of the Jacobain matrix is still needed toform the preconditioner. The linearizing process may alsogenerating additonal numerical errors. Here we presentan alternative way called pseudo-transient continuation byadding first and second order time derivative to the equa-tion and advancing the resulting time-dependent equationto steady state. Therefore, only the stiffness matrix itself isinvolved. An efficient way is developed to initialize the sys-tem and dynamically precondition the iterative solve. Thesolve is accurate and the symmetric structure of periodicboundary condition is well preserved.

Jin ChenPrinceton Plasma Physics Laboratoryjchen@pppl.gov

CP26

Title : Fast and Accurate Methods with DomainEmbedding

In this lecture, we will present some fast and accurate algo-rithms for solving several types of partial differential equa-tions (pdes) in simple geometries. The class of pdes in-volved may involve both, constant and non-constant co-efficient pdes and the geometries both, two- and three-dimensional. Adaptation of these algorithms to complexgeometries will be discussed and results on applicationsusing these methods will be presented. This is an ongoingwork.

Prabir DaripaTexas A&M UniversityDepartment of Mathematicsprabir.daripa@math.tamu.edu

CP26

For the Inf-Sup Condition on Mesh-Dependent

Norms on a Concave Polygon

In this talk I will discuss about the Babuska-Brezzi(inf-sup)condition when certain mesh-dependent norms are consid-ered on a concave polygon in the plane. The model problemis the Laplace problem with zero boundary condition on apolygon.

Sungkyu ChoiPOSTECHchead@postech.ac.kr

Jae Ryong KweonPohang University of Science and TechnologyKoreakweon@postech.ac.kr

CP26

An h-p Adaptive Strategy for Wave-Like Functions

The hp version of the finite element method is an adaptivefinite element approach in which adaptivity occurs in boththe size, h, of the elements and in the order, p, of theapproximating piecewise polynomials. The objective is todetermine a distribution of h and p that minimizes theerror using the least amount of work in some measure. Wepresent a strategy for selecting between h and p refinementfor functions exhibiting wave-like behaviour.

William F. MitchellNational Institute of Standards and TechnologyMathematical and Computational Sciences Divisionwilliam.mitchell@nist.gov

Eite TiesingaAtomic Physics DivisionNational Institute of Standards and Technologyeite.tiesinga@nist.gov

CP27

New Eigensolvers for Large Scale Nanoscience Sim-ulations

We present results for new iterative eigensolvers based onconjugate gradients and Jacobi-Davidson in the context ofsemi-empirical plane wave electronic structure calculations.These new methods give significant speedup over existingconjugate gradient methods used in electronic structurecalculations. The new methods will be demonstrated forCdSe quantum dots as well as quantum wires constructedfrom layers of InP and InAs. These systems are studiedin the context of a semi-empirical potential where we typ-ically solve for a few states around the gap allowing us tostudy large scale nanaosytems. The parallelization of thisapproach will also be discussed as well as scaling results tolarge processor counts.

Stanimire TomovInnovative Computing Laboratory, Computer ScienceDeptUniversity of Tennessee, Knoxvilletomov@cs.utk.edu

Christof VoemelLawrence Berkeley National Laboratoryvoemel@eecs.berkeley.edu

Julien LangouThe University of Tennessee

CS07 Abstracts 81

langou@cs.utk.edu

Andrew M. CanningLawrence Berkeley National Laboratoryacanning@lbl.gov

Lin-Wang WangLawrence Berkeley National Lablwwang@lbl.gov

Jack J. DongarraDepartment of Computer ScienceThe University of Tennesseedongarra@cs.utk.edu

Osni A. MarquesLawrence Berkeley National LaboratoryBerkeley, CAoamarques@lbl.gov

CP27

On Eigenvalues/Partial Eigenvectors Assignmentin Multi-Input Controllable Linear System

The main objective of the present paper is to utilize thepower of the advanced analysis and synthesis method em-bedded in eigenstructure assignment technique to con-struct a state feedback controller that improves the closedloop systems performance when goals beyond precise eigen-values assignment are to be met, namely partial eigenvec-tors assignment. The proposed procedure fared well to-wards precisely shaping right eigenvectors and implement-ing a feedback controller. The null space of the system ma-trix is exploited to construct parts of the achievable eigen-vectors. The resulting state feedback controller is unique.The existence of a solution to the assignment problem isensured, and an algorithm is presented to design the con-cerned controller. A numerical illustrative example is pre-sented to reveal ease of computations required for designingthe controller

Shady El KashlanLecturer At the Academy for Science and Technologykashlan@aast.edu

CP27

Eigenvalue Grid and Cluster Computations, UsingTask Farming Computing Paradigm and Data Per-sistency

Recent progress has made possible to construct high perfor-mance distributed computing environments, such as com-putational grids and cluster of clusters, which provide ac-cess to large scale heterogeneous computational resources.Exploration of novel algorithms and evaluation of perfor-mance is a strategy research for the future of computa-tional grid and cluster scientific computing for many im-portant applications. We adapted the well-known paralleliterative Lanczos method to compute Hermitian eigenval-ues of large sparse matrices for a GRID platform and fora cluster of clusters worldwide deployed between Franceand Japan. Parts of the proposed GRID algorithm usean efficient task-farming computing paradigm, with datapersistency scheduling strategies.

Laurent ChoyINRIA Futurs and CNRS LIFL, Francelaurent.choy@inria.fr

Serge G. PetitonINRIA and LIFL, Universite de Lilleserge.petiton@inria.fr

CP27

Robust and Efficient Solution of Hermitian Eigen-problems Using Primme

PRIMME, or PReconditioned Iterative MultiMethodEigensolver, is a comprehensive, open source software pack-age for solving large, sparse, hermitian eigenvalue prob-lems. We review some of its enhancements since its firstrelease in October 2005, that include complex hermitianeigenproblems, an interface for solving SVD problems,complete Fortran interface, and full interoperability amongthe different operation modes. We present experimental re-sults from two electronic structure applications and fromdata mining showing its robustness and efficiency.

Andreas StathopoulosCollege of William & MaryDepartment of Computer Scienceandreas@cs.wm.edu

CP27

The Use of Bulk Information to Improve The Scal-ability of Parallel Band Gap Computations ForQuantum Dots

We consider the parallel computation of interior eigen-states of large Hermitian matrices arising from plane-wavediscretization of effective single-particle Schrodinger equa-tions. We apply a folded-spectrum approach based on Pre-conditioned Conjugate Gradient (PCG) to compute only asmall number of eigenstates close to the band gap whose lo-cation determines electronic and optical properties of thesystem. We show how to improve the scalability of theeigensolver from observing that the quantum dot bandstates can be well approximated by states of bulk systems.We make use of these cheaply computable bulk eigenstatesto improve the choice of the starting vector and the pre-conditioner for the eigensolver.

Stanimire TomovInnovative Computing Laboratory, Computer ScienceDeptUniversity of Tennessee, Knoxvilletomov@cs.utk.edu

Christof VoemelLawrence Berkeley National LabScientific Computing Group, Computational ResearchDivisioncvoemel@lbl.gov

Lin-Wang WangLawrence Berkeley National Lablwwang@lbl.gov

Jack J. DongarraDepartment of Computer ScienceThe University of Tennesseedongarra@cs.utk.edu

Osni A. MarquesLawrence Berkeley National LaboratoryBerkeley, CAoamarques@lbl.gov

82 CS07 Abstracts

CP27

Computing Eigenvector Derivatives for RepeatedEigenvalues

Eigenvalues and eigenvectors often occur in engineeringproblems. This eigensystem may depend on some param-eter. The sensitivity of the eigenvector with respect toa change of this parameter is expressed by its derivative.Currently, eigenvector derivatives can be computed whenthe eigenvalues themselves, or the first and/or second or-der derivatives of a repeated eigenvalue, are distinct. Weshow how this method can be generalized for an arbitrarymatrix.

Nico van der AaTechnical University of Eindhovenn.p.v.d.aa@tue.nl

Hennie ter MorscheEindhoven University of Technologyh.g.termorsche@tue.nl

Robert MattheijDepartment of Mathematics and Computing ScienceTU Eindhovenr.m.m.mattheij@TUE.nl

CP28

Parameter Optimization Algorithm for DifferentialEquations in Market Return Prediction

We combine an implementation of a state-of-the-art com-putational optimization algorithm, a dynamic initial pa-rameter pool and a system of nonlinear differential equa-tions to describe price dynamics. Given an n-day period ofmarket price (MP) and net asset value (NAV) from day ito day i+n-1, we obtain four optimal parameters in the dif-ferential equations derived by Caginalp. We then solve theinitial value problem to predict MP and return on day i+nor later. The results of our statistical methods in real datasupport the model. We provide out-of-sample predictionthat is more successful than random walk.

Ahmet DuranUniversity of Michigan - Ann Arbordurana@umich.edu

Gunduz CaginalpUniversity of PittsburghDepartment of Mathematicscaginalp@pitt.edu

CP28

The Importance of Rare Events in Kelly’s Algo-rithm

John Kelly’s 1956 paper, A New Interpretation of Informa-tion Rate, describes an algorithm for exploiting inside infor-mation to optimize capital deployment across uncertain op-portunities. Kelly models the inside information as a noisychannel and shows, under fair odds and no transaction fees,that the maximal capital growth rate is precisely the Shan-non information rate of the channel. The algorithm’s op-timal strategy, however, is valid for more general odds andin the presence of transaction fees. A paradox arises inthe general case because the algorithm can place capital atrisk on outcomes with a known negative expected return.This paper provides an alternative derivation of Kelly’s re-sults that emphasizes the cases where such counterintuitive

strategies arise. The explanation lies with the outsized ef-fects of low-probability events in the context of compound-ing investments. We also extend the information-theoreticinterpretation of the maximum capital growth rate to thegeneral case, where transaction fees can be viewed as ad-ditional noise in the channel.

James L. JohnsonComputer Science DepartmentWestern Washington UniversityJames.Johnson@wwu.edu

CP28

Robust Numerical Schemes for Pricing and Hedg-ing Exotic Options

We present numerical schemes for pricing options with non-smooth payoffs, multiple strike prices, and discrete barri-ers. These exotic options induce discontinuities in the so-lution for which Standard numerical methods may causelarge spurious oscillations, thereby giving misleading esti-mates for options valuations and hedging parameters. Theproposed numerical methods do not incur such oscillationswhile efficient to implement on parallel as well as serialmachine. Numerical experiments are presented to demon-strate the robustness of the methods.

Abdul M. KhaliqMiddle Tennessee State UniversityDepartment of Mathematical Sciencesakhaliq@mtsu.edu

CP28

Finite Element Methods with Three Levels forPricing American Put and Call Options

To compute numerically the price and its free boundary ofAmerican options, we present algorithms of finite elementmethods with three levels for the time-marching. Our al-gorithms are based on the Jamshidian equation which isa version of the Black-Scholes equation. We prove theexistence and uniqueness of the numerical solutions at agiven time level. Also, to compare with other methods, wepresent some numerical results obtained through extensivenumerical experiments.

Sunbu KangDepartment of MathematicsKorea Air Force Academysbkang@postech.ac.kr

Yonghoon KwonDepartment of Mathematics, POSTECHykwon@postech.ac.kr

Taekkeun KimFinancial Engineering Dept.Daewoo Securitieskz@postech.ac.kr

CP29

Fct Algorithms for the Euler Equations on Over-lapping Grids

High resolution numerical methods are critical for the effi-cient computation of fluid flow problems. These methodsshould use high order discretizations on smooth portionsof the flows while maintaining physical consistency near

CS07 Abstracts 83

discontinuities. In this talk we discuss the implementationof flux corrected transport (FCT) algorithms on overlap-ping grids with the motivation to investigate monotonicitypreserving methods for fluid flow problems. The algorithmwill be applied to the Euler equations for an inviscid com-pressible gas. Convergence of the method is investigatedusing both the method of manufactured solutions and fora series of simple flow problems. We then present resultsfor a series of problems involving both moving and station-ary obstacles. These results are compared to results ob-tained using a high-resolution Godunov method. Finallythe method is applied to a number of prototype problemsof relevance to the Z-pinch experiments at Sandia NationalLabs including Sedov’s blast wave and Noh’s problem.

Jeffrey BanksSandia National Laboratoryjwbanks@sandia.gov

John ShadidSandia National LaboratoriesAlbuquerque, NMjnshadi@sandia.gov

CP29

Numerical Symmetry Capture

For reliable fluid dynamic simulations the numerical errorsmust be small. Symmetries are fundamental in physicsthat leave a Partial Differential Equation invariant after atransformation. In this paper Lie Groups will be used toextend this philosophy to discretised equations. It will beshown that errors occur due to the breaking of symmetry.We will introduce a new class of SYNC based numericalmethods that eliminate these errors; SYmmetries Numeri-cally Captured.

Alan S. DawesAWE plcalan.dawes@awe.co.uk

CP29

Adaptive and Implicit Immersed BoundaryMethod with Advection-Electrodiffusion

Immersed boundary method is a mathematical and com-putational framework involving the interaction of fluidand structure. Advection-electrodiffusion of ions(solutes)dissolved in fluid in a biological system is considered inthe context of fluid-solute-structure. For a chemical bar-rier across a boundary, a chemical potential is placed foreach solute(ion) along the boundary. An implicit numer-ical scheme is proposed. For numerical accuracy and effi-ciency, adaptive mesh refinement around boundaries is ap-plied. Stokes equations are solved with hybrid approximateprojection method with cell-centered grid. Advection-electrodiffusion equations are solved with the combinationof geometric and algebraic multigrid methods. With advec-tion of the boundaries, advection of ions is observed. Withlocal change of the amplitude of chemical potentials, dif-fusion of each ion across the boundaries is regulated. Theresults show electroneutrality except in space charge layersnear membranes, and agree with the Nernst equation forthe potential difference across membranes.

Pilhwa Lee, Charles S. PeskinCourant Institute of Mathematical Sciencesleep@cims.nyu.edu, peskin@courant.nyu.edu

CP29

A Hybrid Method for Unsteady Aerodynamics

We develop a stable and accurate hybrid method thatcan handle locally highly nonlinear phenomena in complexgeometries as well as efficient and accurate signal trans-portation in domains with smooth flow and geometries.Two separate solvers, one using high order finite differencemethods and another using the node-centered unstructuredfinite volume method is coupled in a truly stable way. Thetwo flow solvers run independently and recieve and send in-formation from each other by using a third coupling code.Exact solutions to the Euler equations are used to verifythe accuracy and stability of the new computational pro-cedure. We also demonstrate the usefulness of the newmethod in a calculation of the flow around a device withcomplex geometry.

Ken MattssonStanford Universitymattsson@stanford.edu

Jan NordstromThe Swedish Defence Research Agency, UppsalaUniversity, KTHjan.nordstrom@foi.se

Gianluca IccarinoCTR, Stanford University, Stanford,CA 94305-3035, USAjops@ctr.stanford.edu

Jing GongDept. of Information Technology,Uppsala University, Swedenjing@it.uu.se

Frank HamCTR, Stanford Universityfham@stanford.edu

Mohammad Shoeybi, Svard MagnusCTR, Center for Turbulence Research,Stanford University, USAshoeybi@stanford.edu, svard@stanford.edu

Edwin van der WeideDepartment of Aeronautics & AstronauticsStanford Universityvdweide@stanford.edu

CP29

Comparison of Different Techniques for the Studyof Nonlinear Laminar Flow Between Parallel Per-meable Disks

The equations describing similarity solutions for flow be-tween infinite parallel permeable disks with equal rates ofsuction or injection at the interface are analyzed. The non-linear ODE is found to admit a solution for all Reynoldsnumber R, using Leray Schauder degree theory. Unique-ness of solution for small Reynolds number is proved an-alytically. The nonlinear ODE is then solved computa-tionally using regular perturbation technique and numeri-cal finite difference method fail for large value of Reynoldsnumber, where as Pade approximation gives converging so-lution for all values of R and this solution shows the disap-perance of boundary layer as R → ∞, and as a consequenceshock is developed. For many practical applications, we

84 CS07 Abstracts

also calculated the skin friction and pressure distribution.The results are found good agreement with the physicaltheory.

Dinesh P AMSRIT, Bangaloredinesh maths@msrit.edu

Karthik AdimurthiM.S.Ramaiah Institute of Technologykarthikaditi@gmail.com

CP30

A Numerical Method for the Simulation of a Grav-itationally Stratified Atmosphere Over a MountainRange

Although long-wavelength gravity waves may have a negli-gible influence on the overall dynamics of the atmosphere,they pose a computational challenge by sharply restrict-ing the time step. We present a new algorithm to solvethe compressible Euler equations using a splitting to sep-arate the fast acoustic dynamics from the slower anelasticdynamics, as well as a strategy based on normal mode anal-ysis to filter out the fastest modes, thereby allowing for alarger time step. UCRL-ABS-223491.

Phillip ColellaLawrence Berkeley National LaboratoryPColella@lbl.gov

Caroline Gatti-BonoLawrence Livermore National Laboratorycbono@llnl.gov

CP30

Simulation of the Climate of the Last 600 Years

We will run the Educational Global Climate Model fromColumbia University for the past six centuries, and com-pare the output with global reconstructions of annual sur-face temperature patterns. The project’s goal is to ver-ify if the mean annual surface temperature of the North-ern Hemisphere in the model results shows any noticeablewarming distinct from natural climate variability.

Luciano FleischfresserOSSM - ATCl fle@alumni.ou.edu

CP30

Modified Finite Difference Schemes for Geophysi-cal Flows

We describe a method to improve both the accuracy andcomputational efficiency of a given finite difference schemeused to simulate a geophysical flow. The resulting modifiedscheme is at least as accurate as the original, has the sametime step, and often uses the same spatial stencil. However,in certain parameter regimes it is higher order. As exam-ples we apply the method to the shallow water equations,the Navier-Stokes equations, and to a sea breeze model.

Don JonesArizona State UniversityDepartment of Mathematicsdajones@math.asu.edu

CP30

Coupling of Ocean Acoustics and Seismic Waves

The interaction of acoustic and seismic waves with geo-metric features such as bathymetry is of great practicalinterest. Using a newly developed finite difference tech-nique for wave propagation we are studying and evaluatinga number of problems with interacting acoustic and elas-tic materials. Results from parallel computations involvingvery large data sets will be reported.

Stefan NilssonLawrence Livermore National LaboratoryCenter for Applied Scientific Computingnilsson2@llnl.gov

CP30

Numerical Adjoints, Ffts and Generalized LinearStability

A generalized (finite-time) linear hydrodynamic stabilitytheory has recently been developed and shown to providea theoretical explanation of observed transition events atodds with predictions from traditional asymptotic theory.However, creating a numerical model, ab initio, to applythis methodology to different flow regimes requires consid-eration of important numerical aspects. In this talk, theseissues will be considered and illustrated using an examplefrom atmospheric dynamics.

Matt TearleUniversity of Coloradomatthewt@colorado.edu

CP31

Self-Consistent Hartree-Fock Calculations for theEffect of Pressure on the Electronic Structure ofDiamond

A self-consistent Hartree-Fock formalism on the basis ofsemi-empirical INDO (Intermediate Neglect of DifferentialOverlap) Hamiltonians has been used to study the elec-tronic and pressure dependent properties of diamond. Theincrease of pressure on diamond is predicted to cause anincrease of the valance and conduction band widths witha decrease of the direct band gap, an increase of the elec-tronic occupation probability for p orbital, and a decreaseof x-ray scattering factors.

Mudar A. Abdulsattarministry of science and technology Baghdad-Iraqmudarahmed3@yahoo.com

Ibtesam Radi, Ahmed Abdul-LettifCollege of Science, Babylon University, Hilla, Iraqmudarahmed3@yahoo.com, abdullettif@yahoo.com

CP31

Simple Numerical Ab-Initio Program for MolecularOrbital Calculations

A concise simple numerical ab-initio program for molecularcalculations is written using trapezoidal rule for carryingmolecular Hartree-Fock integrals. the program accepts anykind of basis functions to perform the calculations suchas Gaussian or Slater type functions or numerically inputfunctions. In spite of long execution time, the programis very limited in its size. The program can be used as a

CS07 Abstracts 85

whole or to check single values of molecular integrals.

Mudar A. Abdulsattarministry of science and technology Baghdad-Iraqmudarahmed3@yahoo.com

Hayde AbduljalilBabylon Univercsity- IRAQmudarahmed3@yahoo.com

Khalid AhmedAl-mustansiriya Unuversity- IRAQmudarahmed3@yahoo.com

CP31

Computational Workflow for Petaflops-Scale Bio-Molecular Simulations: Opportunities and Chal-lenges

Petaflops-scale processing capabilities are essential forbreakthrough bio-molecular simulations, which are widely-used in many fields including bio-fuel and protein-foldingsimulations. Supercomputing systems at this scale willhowever be significantly different from conventional clus-ter systems, and are likely to have unique combinations ofprocessor, networking and IO characteristics. This talk willoverview the key workflow components of a bio-molecularsimulation. We will also identify opportunities and chal-lenges for large-scale system simulations (>500,000 atoms)on Petaflops-scale supercomputers.

Pratul Agarwal, Jeffrey Vetter, Sadaf R. AlamORNLagarwalpk@ornl.gov, vetter@ornl.gov, alamsr@ornl.gov

CP31

Estimating Accuracy in Molecular Dynamics Sim-ulation

In molecular dynamics, accuracy and efficiency of a numer-ical method should be measured with respect to statisti-cal averages, rather than deviations from an “exact trajec-tory”. In this talk I will survey some results from backwarderror analysis and show how (under certain assumptions)these results can be applied to compute estimates of the er-ror in averages from molecular dynamics simulations. Re-sults from several test problems will be explored includingexamples from constant temperature molecular dynamics.

Stephen BondUniversity of Illinois Urbana ChampaignDepartment of Computer Sciencesdbond@uiuc.edu

CP31

Molecular Property Prediction Using KernelMolecular Dynamics

Molecular dynamics can be used to simulate the behav-ior of molecular structures with high accuracy on a smallscale. Supervised learning methods can be used to makechemical property predictions less accurately but on a largescale. We propose the marriage of these two methods usinga Support Vector Machine kernel function. We introducea novel kernel function which incorporates molecular dy-namics. We apply the approach to existing datasets to test

its effectiveness.

William BrownComputational BiologySandia National Laboratorieswmbrown@sandia.gov

Shawn MartinComputational Biology Dept.Sandia National Laboratoriessmartin@sandia.gov

CP31

Using the Method of Weighted Residuals to Com-pute Potentials of Mean Force

The potential of mean force (PMF) describes the changein free energy along a reaction coordinate and determinesthe strength and likelihood of association in molecular sys-tems. We propose a general framework for approximat-ing the PMF in conformational space. This framework,based on the method of weighted residuals, can be viewedas a generalization of thermodynamic integration and di-rect histogram methods. Comparisons between the newweighted residual methods, thermodynamic integration,and WHAM are performed.

Eric C. Cyr, Stephen BondUniversity of Illinois Urbana ChampaignDepartment of Computer Scienceericcyr@uiuc.edu, sdbond@uiuc.edu

CP32

A Primal-Dual Interior-Point Method for DynamicConstrained Global Minimization in Thermody-namic Phase Calculations

The global minimization of non-convex energy functionsarises in thermodynamic calculations where phase equilib-rium is characterized by the convex envelope of the en-ergy function. A primal-dual interior-point algorithm ispresented for computing the convex envelope. It is ex-tended then to evolutive problems with time-dependentconstraints, by coupling the optimization problem withdifferential equations. The time discretization of thedifferential-algebraic system leads to a block-structuredKKT system. Applications to the modeling of atmosphericparticles are given.

Alexandre Caboussat, Neal AmundsonUniversity of Houstoncaboussat@math.uh.edu, amundson@uh.edu

John SeinfeldCalifornia Insititute of Technologyseinfeld@caltech.edu

Jiwen HeDepartment of MathematicsUniversity of Houstonjiwenhe@math.uh.edu

CP32

Inexact Sqp Methods for Equality Constrained Op-timization

The high cost of step computations in sound nonlinear op-timization algorithms presents a number of challenges for

86 CS07 Abstracts

their application to large-scale equality constrained prob-lems, e.g., those defined by systems of partial differentialequations. We outline a simple set of easily calculable crite-ria to evaluate any potential primal-dual step as an inexactSequential Quadratic Programming step, the incorporationof which into any algorithm will lead to a globally conver-gent method allowing for relatively cheap step computa-tions.

Richard H. ByrdUniversity of Coloradorichard@cs.colorado.edu

Jorge NocedalDepartment of Electrical and Computer EngineeringNorthwestern Universitynocedal@eecs.northwestern.edu

Frank E. CurtisNorthwestern Universityfecurt@gmail.com

CP32

Uncertainty Estimation for Large-Scale Ill-PosedInverse Transport Problems

We consider the problem of estimating the uncertainty inthe initial condition field of a convection-diffusion problemdescribing the transport of atmospheric contaminants. Theuncertainty results from measurement of the contaminantconcentration at a limited number of sensors. Estimationof the covariance matrix is facilitated by a low rank (trun-cated Lanczos) approximation of the compact part of theHessian matrix of the inverse problem, under the assump-tion of Gaussian statistics. Examples demonstrate the abil-ity to estimate uncertainty at a small multiple of the costof solving the forward problem.

Pearl FlathUniversity of Texas at Austinpflath@gmail.com

Judy HillSandia National Laboratoriesjhill@sandia.gov

Volkan AkcelikStanford Linear Accelerator Centervolkan@slac.stanford.edu

Karen E. WillcoxMITkwillcox@MIT.EDU

Lucas WilcoxUniversity of Texas at Austinlucasw@ices.utexas.edu

Bart G. Van Bloemen WaandersSandia National Laboratoriesbartv@sandia.gov

Omar GhattasUniversity of Texas at Austinomar@ices.utexas.edu

CP32

Optimization of the Geometry of Materials

Materials scientists are interested in determining the ge-ometry of a material in its ground-state configuration inorder to predict its physical and chemical properties. Ourresearch seeks to determine which optimization methodsare the most effective for the geometry optimization prob-lem (also known as the structural relaxation problem) offinding a low-energy configuration of a material. In thistalk, we compare the performance of several quasi-Newtonand nonlinear conjugate gradient methods on various ma-terials.

Suzanne M. ShontzDept of Computer Science and EngineeringThe Pennsylvania State Universityshontz@cse.psu.edu

Yousef SaadDepartment of Computer ScienceUniversity of Minnesotasaad@cs.umn.edu

CP32

An Optimization Procedure For Model UpdatingVia Physical Parameters

The matrices of many finite elements models can be ex-pressed in terms of physical parameters and known sub-structure matrices. A new optimization-based method isproposed for updating of such models by improving thephysical parameters only. Thus, the important structuralproperties, including the connectivity, structure, are pre-served by the updating. An appropriate gradient formulais developed for the solution of the corresponding optimiza-tion problem.

Vadim O. SokolovDepartment of MathematicsNorthern Illinois Universitysokolov@math.niu.edu

Daniil SarkissianRussian Academy of SciencesInstitute of Computational Mathematicssarkiss@math.niu.edu

Biswa N. DattaNorthern Illinois Universitydattab@math.niu.edu

MS0

Pathway Modeling of Shewanella DenitrificansOS217

The bacterium Shewanellas ability to reduce compounds ofseveral metals, some of which may be toxic to humans andto other organisms, make it an ideal candidate for biore-mediation of contaminated areas. The metabolic pathwaymodeling software, Pathway Tools, was used to model spe-cific metabolic pathways of the bacterium Shewanella den-itrificans OS217. The results of this study are expected toprovide insight into Shewanella metabolism and to assistin the design of bioremediation programs.

Jessica McGarityWofford CollegeMcGarityJD@Wofford.Edu

CS07 Abstracts 87

MS0

Adaptive Temporal Integration of ODEs with In-terval Computations

The area of Interval Computations is of growing interestfor rigorous and error bounded computations. By usinginterval arithmetic routines in the Matlab toolbox Intlab,error bounds can be propagated throughout an algorithmto yield reliable enclosures of solutions. We examine theuse of interval arithmetic applied to adaptive temporal in-tegration of stiff ODEs and solutions to nonlinear systems.

Michael P. PetitoClarkson Universitypetitomp@clarkson.edu

MS0

Resolving Systematic Errors in using Discrete Datato Fit Continuous Functions

We recorded the motion of oscillating springs, fit continu-ous functions to data sequences using Excel Solver to fit pa-rameters by minimizing the sum of squared error, and an-alyzed the patterns of the residuals. The residuals showedsystematic errors indicating our theoretical model or datawere flawed. Our procedure for examining the error allowedus to verify our theoretical model using discrete data, andinvestigate the sources of systematic error in the model ordata.

Megan Elise Selbach-AllenUnited States Naval Academym095835@usna.edu

MS1

Scalable High Fidelity Modeling of SemiconductorDevices

Abstract not available at time of publication.

Robert J. HoekstraSandia National Laboratoriesrjhoeks@sandia.gov

MS1

High Performance Modeling of Circuits Using theMultitime PDE Algorithm

Abstract not available at time of publication.

Eric KeiterSandia National Laboratorieserkeite@sandia.gov

MS1

Novel Algorithms SPICE Diego for Circuit Simu-lation

Abstract not available at time of publication.

Rui ShiUniversity of California San Diegorshi@cs.ucsd.edu

MS2

Specialized Computing Architectures for Biological

Computations

This talk describes the current state of the art in biomolec-ular simulation and explores the potential role of high-performance computing technologies in extending currentcapabilities. Efforts within our own lab to develop novelarchitectures and algorithms to accelerate molecular dy-namics simulations by several orders of magnitude wouldbe described, along with work by other researchers pursu-ing alternative approaches. If such efforts ultimately provesuccessful, one might imagine the emergence of an entirelynew paradigm in which computational experiments taketheir place alongside those conducted in ”wet” laboratoriesas central tools in the quest to understand living organismsat a molecular level.

Marty M. DeneroffD.E. Shaw Research, LLCmarty.deneroff@deshaw.com

MS2

Climate Modeling at the Petaflop Scale UsingSemicustom Computing

We present the performance requirements of an atmo-spheric general circulation model at ultra-high resolutionand describe alternative technological paths to realize a so-lution in the relatively near future. It is estimated that acredible kilometer scale atmospheric model would requireat least a sustained ten petaflop computer to provide sci-entifically useful climate simulations. Analysis shows thatembedded processor technology could be exploited to tai-lor a custom machine designed to ultra-high climate modelspecifications at surprisingly affordable cost and power con-siderations.

Leonid Oliker, Michael Wehner, John ShalfLawrence Berkeley National Laboratoryloliker@lbl.gov, mfwehner@lbl.gov, jshalf@lbl.gov

MS2

Domain-Oriented Processors for Power-EfficientMulti-PetaFLOP HPC

This informal talk discusses the potential and outlines onepossible design for a highly efficient petascale system (10-petaFLOPS peak and roughly 1 petaFLOPS sustained)oriented towards important high-performance parallel com-puting problems such as climate modeling. The proposedsystem is at least one order of magnitude more energy ef-ficient than extrapolations from existing HPC cluster sys-tems for two reasons: 1) a sharp focus on an applicationdomain for which local mesh topologies permit efficient,low-contention communications, and 2) utilization of con-figurable processor technology derived from high-efficiency,multiple processor applications in embedded consumer andcommunication products.

Chris RowenCEOTensilica Inc.rowen@tensilica.com

MS2

MDGRAPE-3 : A Petaflops Special-Purpose Com-puter for Molecular Dynamics Simulations

We have developed a special-purpose computer systemfor molecular dynamics simulations named MDGRAPE-3,

88 CS07 Abstracts

which has nominal peak performance of 1 PFLOPS. It con-sists of 4,778 fully-customized processors of 216 GFLOPSfor calculations of forces between atoms. The specializa-tion enables highly-parallel operations inside the processorby the ”broadcast memory architecture”. By using manyparallel pipelines at moderate speed of 300 MHz, our pro-cessor consumes a low power of 17 W, or 0.1 W/GFLOPS.

Makot Taiji, Tetsu Narumi, Yosuke OhnoRIKEN, Japantba@riken, tba@riken, tba@riken

MS3

Bifurcation Analysis of a Liquid State Theory:Multiple Solutions and Phase Transitions

This talk presents bifurcations of the Ornstein-Zernike(OZ)equation with hypernetted chain and Perkus-Yevick clo-sures using several intermolecular potentials. We showthat spinodal solution branches, precursors to a liquid-vapour phase transition, cannot be reproduced numeri-cally, and that the existence of a so-called no-solution re-gion causes fold bifurcations along the vapour isothermalsolution branch when density is used as the bifurcationparameter. This provides an explanation for previous in-conclusive attempts to compute near-critical solutions withNewton-Picard methods.

Robert BeardmoreDepartment of MathematicsImperial College Londonr.beardmore@imperial.ac.uk

MS3

Advanced Numerical Methods for Density Func-tional Theories

We discuss numerical methods developed for the solutionof Density Functional Theories for inhomogeneous fluidsin complex 3D geometries. The nature of the equationsmakes application of generic parallel iterative solvers lessthan optimal. We discuss a Schur complement based ap-proach that improves the performance and stability of themethods. Solution complexity and identification of phasetransitions with arc-length continuation methods will bediscussed in the context of a variety of applications.

Andrew SalingerApplied Computational Methods Dept, Sandia NationalLabsagsalin@sandia.gov

Michael A. HerouxSandia National Laboratoriesmaherou@sandia.gov

Laura FrinkSandia National Labsljfrink@sandia.gov

MS3

Why Sampling Efficiency is the Key to UsingMolecular Theory as an Implicit Solvent for MonteCarlo Molecular Simulations

Simulations of mixtures with at least one large componentin a small solvent are challenging. The larger componentsare the focus of the simulation, but the solvent has signif-

icant effects. Implicit solvent methods trade off accuracyin solvent effects for computational speed. In Monte Carlo(MC) simulations, convergence depends on efficiently sam-ple phase space. We discuss how new MC methods forsampling coupled with a molecular theory based implicitsolvent may provide a route for MC based investigation ofthese systems.

Marcus MartinSandia National Laboratoriesmarmart@sandia.gov

MS3

Morphometric Approach: Theory and Applicationin Biophysics

Fluids in confined geometries develop an inhomogeneousstructure and their thermodynamic properties depend ina complicated way on the geometry. The morphometricapproach discussed here allows one to transfer the insightgained in simple geometries to complicated ones. This isaccomplished by the separation of the grand potential intofour geometrical measures, describing the shape of the con-finement, and corresponding thermodynamic coefficients.We discuss protein folding as an application of the mor-phometric approach.

Roland RothMax-Planck-Institut fuer Metallforschung, Heisenbergstr.,GeGermanyemail@tba

MS4

An Asynchronous Parallel Generating Set SearchAlgorithm for Handling Nonlinear General Con-straints

Many real-life optimization problems present formidablechallenges despite having a relatively small number of inde-pendent variables. Difficulties can arise from nonsmooth-ness, discontinuities, and noise. Further, function evalu-ations typically involves calling unwieldy CPU-intensivesimulation software that may periodically crash. In thiscontext, we present a globally convergent derivative-freemethod for nonlinear programming based on generatingset search. Linear constraints are handled using conform-ing search directions. Several options for handling nonlin-ear constraints are explored, including an augmented La-grangian approach. All methods are implemented asyn-chronously in parallel. We present extensive test resultsusing the CUTEr test set as well as real-life applications.

Tamara G. KoldaSandia National Laboratoriestgkolda@sandia.gov

Joshua D. GriffinComputational Sciences and Mathematics ResearchSandia National Laboratoriesjgriffi@sandia.gov

MS4

Surface Structure Determination of Nanostruc-tures Using a Mesh Adaptive Optimization Method

Many properties of nanostructures depend on the atomicconfiguration at the surface. One common technique used

CS07 Abstracts 89

for determining this surface structure is based on the lowenergy electron diffraction (LEED) method, which uses asophisticated physics model to compare experimental re-sults with spectra computed via a computer simulation.While this approach is highly effective, the computationalcost of the simulations can be prohibitive for large systems.In this work, we propose the use of generalized patternsearch methods in combination with a simplified physicssurrogate for the full fidelity physics model. The gener-alized pattern search method handles both discrete andcontinuous variables, which allows the simultaneous opti-mization of the atomic coordinates as well as the chemicalidentity. In addition, the calculation time of the surrogatescales linearly with the number of atoms on the unit cell(N), compared to the N3 scaling behavior of the full LEEDcalculation. We will present some numerical results basedon this simplified physics surrogate within a mesh adaptivedirect search (MADS) algorithm.

John Dennis, Jr.Rice Universitydennis@rice.edu

Aran Garcia-LekueDonostia International Physics Centeragarcia-lekue@lbl.gov

Mark AbramsonAFITmark.abramson@afit.edu

Juan C. MezaLawrence Berkeley National LaboratoryJCMeza@lbl.gov

MS4

Function Approximation Algorithms for Local andGlobal Optimization Including Applications to Ex-pensive Engineering Simulations

Global optimization methods are often necessary for com-plex simulation models because there is no guarantee theproblem is unimodal. We discuss numerical comparisons ofvariety of existing global optimization methods with localoptimization methods implemented with multi-start. Wewill also present convergence theorem and numerical re-sults for a new method that is a hybrid between a globaland a multistart method, which outperforms alternativealgorithms on number of multimodal test problems andexpensive engineering simulations.

Rommel G. RegisCornell Theory Center, Cornell Universityrgr6@cornell.edu

Christine ShoemakerCornell Universitycas12@cornell.edu

MS4

Optimization of Simulation-Based OptimizationProblems with Constraints on the ComputationalBudget

We consider simulation-based optimization problems wherethe function evaluation is expensive and the computationof derivatives is not feasible. Pattern-based algorithmsor surrogate-based algorithms, which repeatedly build and

optimize over cheap-to-evaluate approximations of the ob-jective function, often make unsatisfactory progress in re-ducing the function within a fixed computational budget.We propose an algorithm that finds an approximate lo-cal minimizer in fewer function evaluations than currentderivative-free alternatives.

Stefan M. WildCornell UniversitySchool of Operations Research & IEsmw58@cornell.edu

Jorge J. MoreArgonne National LaboratoryDiv of Math & Computer Sciencemore@mcs.anl.gov

MS5

A Regularized Gauss-Newton Method for Ill-PosedNonlinear Problems Applied to Diffuse Optical To-mography

Many reconstruction problems take the form of a nonlin-ear least-squares problem for a set of parameters. Thetraditional methods, damped Gauss-Newton (GN) andLevenberg-Marquardt (LM), are generally effective butthey require a considerable number of function and Ja-cobian evaluations to determine the correct step lengthand/or damping parameter. To deal with ill-conditionedJacobians and (usually) noise in the data, we propose aregularized, trust-region-based Gauss-Newton approach fordetermining search directions. Our method systematicallyevaluates the potential contribution of each of the spec-tral components corresponding to the GN-direction andconstructs the new direction relative to this contributionwithin the confines of a trust-region. Examples show thesuccess of our method in minimizing function evaluationswith respect to other well-known methods.

Misha E. KilmerTufts Universitymisha.kilmer@tufts.edu

Eric De SturlerVirginia Techsturler@vt.edu

MS5

On the Use of Krylov-Secant Updates to Accelaratethe Convergence of Nonlinear Ill-posed Problems

This work proposes an inexact Newton-Krylov frameworkbased on Krylov-secant updates. This entails to recycle orextrapolate the Krylov information generated for the solu-tion of the current Jacobian equation to perform a sequenceof secant steps restricted to the Krylov basis. In otherwords, the Newton step is recursively composed with Broy-den updates constrained to the reduced Krylov subspace.This is repeated until no further decrease of the nonlinearresidual can be delivered, in which case, a new nonlinearstep yielding another Jacobian system is performed.

Adolfo RodriguezTBAtba@tba.edu

Mary F. WheelerCenter for Subsurface ModelingUniversity of Texas at Austin

90 CS07 Abstracts

mfw@ticam.utexas.edu

Hector KlieCenter for Subsurface Modeling, UT Austinklie@ices.utexas.edu

MS5

A Hybrid Optimization Approach for the Auto-mated Parameter Estimation Problem

We propose two hybrid optimization approaches based onthe coupling of the simultaneous perturbation stochasticapproximation (SPSA) (a global and derivative free opti-mization method) with two local and derivative-dependentoptimization methods: (1) the globalized Newton-Krylovinterior-point and, (2) the global Levenberg-Marquardt .The former implies the generation of a surrogate modelwhereas the latter gradually incorporates derivative infor-mation as sufficient progress is made towards the solution.Numerical examples show their appealing capabilities forparameter estimation

Carlos QuinteroUniversity of Texas at El pasotba@utep.edu

Leticia VelazquezUniversity of Texas-El Pasoleti@math.utep.edu

Mary F. WheelerCenter for Subsurface ModelingUniversity of Texas at Austinmfw@ticam.utexas.edu

Miguel ArgaezUniversity of Texas at El pasomar@math.utep.edu

Hector KlieCenter for Subsurface Modeling, UT Austinklie@ices.utexas.edu

MS6

Model Reduction and Mode Computation forDamped Resonant MEMS

In the design of resonant micro-electro-mechanical systems,controlling the amount of damping is critical. Simulationswhich incorporate realistic damping models typically leadto non-Hermitian problems which depend nonlinearly on afrequency parameter. In this presentation, we discuss ourwork on developing methods that use the structure of thedamped model equations to efficiently compute modes andreduced order models of these problems. We illustrate ourmethods with models of thermoelastic damping in resonantmicrostructures.

David BindelCourant Institute of Mathematical SciencesNew York Universitydbindel@cims.nyu.edu

MS6

AMLS Method for Sparse Eigenvalue Problems

We describe an efficient implementation and present a per-

formance study of an algebraic multilevel sub-structuring(AMLS) method for sparse eigenvalue problems. We as-sess the time and memory requirements associated withthe key steps of the algorithm, and compare it with theshift-invert Lanczos algorithm in computational cost. Oureigenvalue problems come from two very different areas:the accelerator cavity design and the normal mode vibra-tional analysis of the polyethylene particles. We show thatthe AMLS method is very competitive with the traditionalmethod in broad application areas, especially when largenumbers of eigenvalues are sought.

Weiguo GaoFudan University, Chinawggao@fudan.edu.cn

Xiaoye S. LiComputational Research DivisionLawrence Berkeley National Laboratoryxsli@lbl.gov

Zhaojun BaiUniversity of Californiabai@cs.ucdavis.edu

Chao YangLawrence Berkeley National LabCYang@lbl.gov

MS6

Modal Dynamic Solutions - Current State andChallenges

This presentation will briefly review the concept of modaldynamic solutions and present some of their structuralengineering industry use, a topic not well understood byacademia. The state of the current technology and re-maining numerical and computational challenges will alsobe discussed.

Louis KomzsikUGSkomzsik@ugs.com

MS6

Solving Structural Eigenproblems with KKT Ma-trices

Lagrange multiplier techniques are a popular method formodeling constraints in structures stemming from contact,nonlinear rigid elements, inertia relief, and other applica-tions. The resulting KKT matrices are indefinite, posing asignificant challenge for the prevailing eigenvalue solutiontechniques in normal modes and buckling analysis. Thistalk will describe a Lanczos eigensolver which has beenmodified to handle KKT matrices.

Thomas KowalskiMSC.softwaretom.kowalski@mscsoftware.com

MS7

Interoperable Mesh and Geometry Technologies

Interoperable mesh and geometry technologies developedby the ITAPS center allow domain scientists to leverageboth software and the expertise of tool developers. Criticalto our interoperability goal is the creation of the creation

CS07 Abstracts 91

of common interfaces for a wide variety of mesh and geom-etry tools that will allow them to work with each other toprovide fundamentally increased capabilities and to allowapplication scientists to switch among them easily. I de-scribe the current status of our interface definition effort,the tradeoffs required to balance performance and flexi-bility, the tools used to address language interoperabilityissues, and many of the tools now available through theITAPS interfaces.

Lori A. DiachinLawrence Livermore National Laboratorydiachin2@llnl.gov

MS7

On the Interoperability Between FronTier andOther Scientific Application Software

The FronTier code features high quality tracking of a dy-namically moving interface and the coupling of between thefront and interior solutions. A combined operation betweenfront tracking and other adapted mesh software such as theOverture and KIVA codes enables highly resolution scien-tific applications such as the study of combustion problems.

Xiaolin LiDepartment of Applied Math and StatSUNY at Stony Brooklinli@ams.sunysb.edu

James G. GlimmSUNY at Stony BrookDept of Applied Mathematicsglimm@ams.sunysb.edu

Wurigen BoSUNY Stony Brookbowrg@ams.sunysb.edu

Zhiliang XuBrookhaven National LabSUNY Stony Brookxuzhi@bnl.gov

Brain FixSUNY Stony Brookbrian@ams.sunysb.edu

MS7

Adding Adaptive Mesh Control to Fusion and Ac-celerator Applications

The ability to support adaptive computations starting fromexisting non-adaptive analysis programs requires determin-ing where and how the mesh needs to be improved andthen executing those mesh improvements. This presenta-tion will describe a tool capable of performing the meshmodification needed to alter a given mesh to match a spec-ified anisotropic mesh size field. Its use in the creation ofadaptive analysis loops for multiple applications will alsobe presented.

Xiaojuan Luo, Mark S. ShephardRensselaer Polytechnic InstituteScientific Computation Research Centerxluo@scorec.rpi.edu, shephard@scorec.rpi.edu

Onkar Sahni

Rensselaer PolytechnicScientific Computation Research Centerosahni@scorec.rpi.edu

Andrew BauerScientific Computation Research CenterRensselaer Polytechnic Instituteacbauer@scorec.rpi.edu

MS7

Applications of the TSTT Geometry, Mesh, andRelations Interfaces

The Interoperable Tools for Advanced Petascale Simula-tions (ITAPS) center has developed API specifications forinterfaces to geometry, mesh, and relations data. Theseinterfaces allow the construction of tools which operate onthe associated data, without depending on one particularimplementation of those interfaces. These interfaces alsoallow the assembly of advanced components and servicesbased on third party tools interacting though these inter-faces. This presentation will describe several such compo-nents and services, including partitioning/load balancingand parallel mesh generation. Geometry and mesh sup-port for shape optimization will also be described.

Timothy J. TautgesArgonne National Laborytautges@engr.wisc.edu

MS8

A Parallel And Generic Algebraic Multigrid Algo-rithm Based on Agglomeration

Sparse matrices obtained from finite element discretiza-tions exhibit a lot of structure (e.g., discretization of three-component system with linear finite elements and point-wise ordering) already known at compile time. The parallelalgebraic multigrid algorithm based on agglomeration pre-sented is capable of exploiting this structure using genericprogramming techniques. This leeds to shorter setup times,e.g., for systems of linear equations. And the smoothers,coarse grid solvers and surrounding preconditioned Krylowmethods become more efficient due to the knowledge of thestructure.

Peter BastianIPVSUniversity Stuttgartpeter.bastian@ipvs.uni-stuttgart.de

Markus BlattUniversity Stuttgartmblatt@hal.iwr.uni-heidelberg.de

MS8

Scaling Multigrid Libraries to 100K Processors

In this talk, we will first overview the basic issues associ-ated with developing parallel multigrid methods, outliningsome of the techniques used to overcome these problems.The remainder of the talk will focus on additional issuesthat arise when confronting architectures with more than100K processors (e.g., BlueGene/L), especially when de-veloping multigrid libraries such as hypre. In particular,we will describe our new assumed partition algorithm and

92 CS07 Abstracts

new interpolation schemes for algebraic multigrid.

Robert FalgoutCenter for Applied Scientific ComputingLawrence Livermore National Laboratoryrfalgout@llnl.gov

MS8

High Performance Parallel Multigrid for Large-Scale Electromagnetics Simulations

Parallel multigrid for large-scale electromagnetics simula-tions presents unique challenges, due to the need to simul-taneously address parallel and algorithmic performance.System resources are often constrained because of demandsfrom other parts of the application, coarse-level problemscan have large communication to computation ratios, andload-balancing of the linear systems may be optimized forsomething other than the linear solver. We discuss our ap-proaches to these challenges, and present numerical resultson thousands of processors.

Jonathan J. HuSandia National LaboratoriesLivermore, CA 94551jhu@sandia.gov

MS8

Scalable Parallel Multigrid for Finite ElementComputations

The hierarchical hybrid grids framework combines unstruc-tured FE meshes with structured refinement to achieveexcellent performance on current supercomputer architec-tures. Scalability is achieved by using multigrid as a veryefficient solver and a very careful implementation thatexploits systematically the structuredness of subgrids toachieve excellent node performance. In this talk we willpresent a scale-up study on a 4000 processor SGI altix sys-tem.

Tobias GradlUniversitat Erlangentobias.gradl@informatik.uni-erlangen.de

Ben BergenLos Alamos National Laboratorybergen@lanl.gov

Ulrich J. RuedeUniversity of Erlangen-NurembergDepartment of Computer Science (Simulation)ruede@cs.fau.de

MS9

Mathematical Modeling and Computer Simulationfor Foamy Oil

There exist nearly one trillion barrels of heavy oil inVenezuela. China has a project with orimulsion produc-tion of 6 million tons per year, and expects to have moreprojects like this. Two crucial issues must be addressedbefore or during designing these projects: What is a suit-able method to evaluate foamy oil driven mechanism thatplays a major role during such oil recovery, and how do weget a reasonable number of ultimate oil recovery? Unfortu-nately, it is still very difficult to give good explanations forthese two issues although several studies were performed.

This talk attempts to present better explanations for thesetwo issues using experimental results, mathematical mod-eling, and numerical simulations. This is a joint work withRuihe Wang, Jishun Qin, and Ming Zhao.

Zhangxin ChenSouthern Methodist Universityzchen@mail.smu.edu

MS9

A Higher Order Spectral Finite Volume Methodfor Atmospheric Flows

Advection plays a fundamental role in atmospheric dynam-ics. In many atmospheric transport problems, it is essen-tial to correctly calculate the 3-dim advective transport ofatmospheric constituents over the globe. High-order nu-merical methods offer the promise of accurately capturingthese advective processes in atmospheric flows and havebeen shown to efficiently scale to large numbers of proces-sors. The spectral finite volume (SFV) method was de-veloped by Wang for conservation laws and has been usedby Choi et al. for ocean modeling. Recently, we devel-oped a transport scheme based on a high-order nodal SFVon cubed-sphere which relies on a flux-corrected transport(FCT) scheme to enforce monotonicity. The reconstruc-tion procedure which we developed avoids the expensivecalculation of the inverse of a matrix used by Choi et al.We are currently working to apply this approach to anSFV based nonlinear shallow water model in curvilinear-coordinates on a cubed-sphere. In this talk, we will discussglobal transport scheme combined with FCT. We also an-ticipate presenting our SFV based results for shallow watermodel.

Vani CheruvuNational Center for Atmospheric Researchvani@ucar.edu

MS9

Characteristic Methods for Reservoir Simulation

Fluid transport is a major process that controls many reser-voir simulation applications. Fluid transport is modeledvery well by flow along characteristics of advection partof the differential operator. Characteristic methods thatutilize these flow directions can effectively predict fluidtransport without introducing artificial diffusion phenom-ena. Finite element and wavelet Eulerian-Lagrangian lo-calized adjoint methods (ELLAM) will be presented , withtheir analysis and computational examples. This is a jointwork with Jiangguo Liu and Hong Wang.

Hong WangUniversity of South CarolinaDepartment of Mathematicshwang@math.sc.edu

Jiangguo LiuColorado State Universityliu@math.colostate.edu

Richard E. EwingTexas A&M Universityrichard-ewing@tamu.edu

MS9

Numerical Analysis and Adaptive Computation for

CS07 Abstracts 93

Solutions of Elliptic Problems with Randomly Per-turbed Coefficients

We develop and analyze an innovative numerical methodfor computing solutions to the Poisson equation with ran-domly perturbed multiscale coefficients in an efficient fa-sion. We derive a posteriori error estimates for the methodand use this to devise an adaptive algorithm for automatictuning of the method parameters such as mesh size andsample size. The goal of the adaptive algorithm is to min-imize the error in the distribution function generated bytaking a desired linear functional of the solutions. Themethod is successfully applied to a problem that arises inoil reservoir simulation.

Donald Estep, Simon TavenerColorado State Universityestep@math.colostate.edu, tavener@math.colostate.edu

Axel MalqvistUniversity of California at San Diegoaxel@cam.ucsd.edu

MS10

Adaptive Multilevel Mesh Refinement for the So-lution of Large Scale Inverse Problems

In this talk we study an efficient method for the solutionof distributed parameter estimation problems. We are par-ticularly interested in problems where the regularizationoperators allow jumps in the solution such as Total Vari-ation and Huber. Even for relatively simple problems thecomputational cost of solving the inverse problems can besubstantial. This is because the forward problem can bedifficult to solve, especially when the coefficients are discon-tinuous. Solving the inverse problem is therefore challeng-ing and advanced computational techniques are needed. Inthis talk we explore the use orthogonal but non-conformingfinite difference or finite volume methods. We show thatthey can be very efficient for the solution of inverse prob-lems and dramatically reducing the computation.

Eldad HaberEmory UniversityDept of Math and CShaber@mathcs.emory.edu

MS10

Multigrid Methods for Optimal Control ProblemsGoverned by Advection Diffusion Equations

Linear-quadratic optimal control problems governed byadvection-diffusion equations arise in a variety of appli-cations. The optimality conditions for these problems leadto large-scale, symmetric indefinite linear systems of equa-tions, which have to be solved iteratively. These systemsinvolve two discretized advection-diffusion equations withadvection in one equation given by the negative advectionin the other. In this talk we discuss multigrid methodsfor these optimality systems and explore differences in be-havior of MG methods applied to a single PDE and MGmethods applied to the optimality system.

Matthias HeinkenschlossRice UniversityDept of Comp and Applied Mathheinken@rice.edu

MS10

Multilevel Methods for Nonlinear Conjugate Gra-dient Methods

We analyze the performance of nonlinear conjugate gradi-ent methods for mesh-based optimization problems. Weshow, in particular, that the use of scaling and limited-memory techniques results in significant improvements inperformance. We present results for both single-processorand multi-processor environments.

Jorge MoreANLmore@mcs.anl.gov

Todd S. MunsonArgonne National LaboratoryMathematics and Computer Science Divisiontmunson@mcs.anl.gov

Jason SarichArgonne National Laboratorysarich@mcs.anl.gov

MS10

Assessing the Performance of Optimization-BasedMultigrid Methods

Many large nonlinear optimization problems are basedupon discretizations of underlying continuous functions.Optimization-based multigrid methods are designed tosolve such discretized problems efficiently by taking explicitadvantage of the family of discretizations. The methodsare generalizations of more traditional multigrid methodsfor solving partial differential equations. We discuss tech-niques whereby the multigrid method can assess its ownperformance, with the goal of adaptively deciding appro-priate levels of discretization.

Stephen G. NashGeorge Mason UniversitySchool of Information Technology & Engineeringsnash@gmu.edu

Robert Michael LewisCollege of William & MaryDept. of Mathematicsrmlewi@wm.edu

MS11

Reduced Order Approaches for Variational DataAssimilation in a Model of the Tropical PacificOcean

A reduced order approach for 4D-Var data assimilation ispresented in the context of a tropical Pacific ocean model.The control space is defined as the span of a few vectorsrepresenting a significant part of the system variability. Itis shown that such an approach can lead to significant im-provements, both in terms of the quality of the solutionand of the computational efficiency. A first step toward anhybrid variational-sequential algorithm is also discussed.

Celine RobertLMC-IMAGGrenoble, Franceceline.robert@imag.fr

Jacques Verron

94 CS07 Abstracts

LEGI, Grenoble, Francejacques.verron@inpg.fr

Eric BlayoUniversity of Grenobleeric.blayo@imag.fr

MS11

Analysis of a POD Approach to Order Reductionin 4D-Var Data Assimilation

The proper orthogonal decomposition method to order re-duction in 4D-Var data assimilation is implemented for atwo dimensional global shallow water model. Specifica-tion of appropriate weights to the snapshots and the normused to quantify the projection error are discussed. A re-duced second order adjoint model is used to perform a Hes-sian condition number analysis in the POD space. A dualweighted procedure based on adjoint sensitivity fields isshown to provide improved results.

Dacian N. DaescuPortland State UniversityDepartment of Mathematics and Statisticsdaescu@pdx.edu

Ionel Michael NavonDepartment of Mathematics and C.S. I.T.Florida State Universitynavon@csit.fsu.edu

MS11

Direct and Inverse POD Model Reduction Appliedto Imperial College Ocean Model

A POD-based reduced model is developed for an advanced3-D adaptive finite element ocean model. The aim of thisstudy is to explore the: (a) feasibility of significant re-duction in the computational cost of an adaptive meshmodel; (b) number of snapshots that contain enough infor-mation to model the behaviour of flow dynamics through-out the data assimilation process; (c) efficiency of the re-duced model in accelerating the inversion procedure; (d)estimation of model error in POD.

Fangxin FangDepartment of Earth Science and EngineeringImperial College London, U.K.f.fang@imperial.ac.uk

Chris.C Pain, Matthew.D Piggott, Gerard.J GormanDepartment of Earth Science and EngineeringImperial College London, U.K.c.pain@imperial.ac.uk, m.d.piggott@imperial.ac.uk,g.gorman@imperial.ac.uk

Ionel Michael NavonDepartment of Mathematics and C.S. I.T.Florida State Universitynavon@csit.fsu.edu

MS11

POD-Based Reduced Order Ocean Modeling andApplications to Variational Data Assimilation

The proper orthogonal decomposition (POD) is a model re-duction technique for the simulation of physical processesgoverned by partial differential equations. In this presen-

tation, the method is applied to a simple reduced gravityocean model in the tropical Pacific. Three issues are dis-cussed here: (1) Numerical comparison of the POD model-ing to the original modeling; (2) Error analysis of the PODmodeling, both from theoretical and numerical aspects; (3)Application to variational data assimilation.

Jiang ZhuInstitute of Atmospheric PhysicsChinese Academy of Sciences,jzhu@mail.iap.ac.cn

MS12

A Posteriori Error Control for Coupled Systems

We extend our a posteriori error analysis for one-way cou-pled elliptic systems to the general setting of coupled ellip-tic systems solved via operator decomposition and single-physics solvers. We decomposte the non-iteration error intoa error contributions from inherited error, single physicsresiduals, and projection error, all computable by formu-lating the appropriate single-physics adjoint problem. Wethen give several numerical illustrations of the features ofthis approach.

Donald Estep, Varis Carey, Simon TavenerColorado State Universityestep@math.colostate.edu, carey@math.colostate.edu,tavener@math.colostate.edu

MS12

An A Posteriori Analysis of Operator Splitting forReaction-Diffusion Ode

In this talk, we present the aposteriori error analysis of anoperator splitting procedure to solve a system of ordinarydifferential equation governing a reaction-diffusion prob-lem. A discontinuous Galerkin Finite Element method isused to solve the resulting analytical splitting. An a priorierror estimate is presented that uses a decomposition of theerror into one that corresponds to the analytical splittingand one that corresponds to the discontinuous GalerkinFinite Element used to numerically solve it. An a posteri-ori analysis is described to derive an error representationthat is computable. The analysis uses the notion of ad-joint problems that correspond to the linearization of theoriginal problem. Some numerical examples will also bepresented.

Donald Estep, Simon Tavener, Victor GintingColorado State Universityestep@math.colostate.edu, tavener@math.colostate.edu,ginting@math.colostate.edu

John ShadidSandia National LaboratoriesAlbuquerque, NMjnshadi@sandia.gov

MS12

Accuracy and Stability of Operator Splitting Meth-ods Applied to Diffusion/Reaction and Convec-tion/Diffusion/Reaction Systems with IndefiniteOperators

In this talk results are reviewed that demonstrate thatcommon second-order operator-splitting methods can ex-hibit subtle instabilities for diffusion/reaction (DR) and

CS07 Abstracts 95

convection/diffusion/reaction (CDR) systems. We evalu-ate the relative accuracy and asymptotic order of accuracyof methods on problems that exhibit an approximate bal-ance between competing component time scales. We con-sider first- and second-order semi-implicit, fully-implicit,and operator-splitting techniques. The problems include apropagating nonlinear DR and CDR wave, a Brusselatorproblem and a simplified CDR chemotaxis model.

John ShadidSandia National LaboratoriesAlbuquerque, NMjnshadi@sandia.gov

MS12

A-Posteriori Analysis of An Operator Decomposi-tion Method for Time-Dependent Transfer of In-formationthough An Interface

We consider operator decomposition methods to be a spe-cial form of operator splitting in which a real or artificialinterface provides a natural partition. We present an a-posteriori adjoint-based analysis of the stability and ac-curacy of an operator decomposition method for a time-dependent reaction-diffusion problem which involves theexchange of information across a physical boundary. Weillustrate our approach with an application to core-edgetransport simulations in fusion modeling.

Tim WildeyDepartment of MathematicsColorado State Universitywildey@math.colostate.edu

MS12

Cost of Accuracy for Coupled Diffusion and Reac-tion Systems

Many applications give rise to coupled and nonlinear math-ematical models. Due to advances in solver technologies,implicit methods have become viable solution alternativesto traditionally-applied operator splitting methods in manyapplication areas. We present results exploring the relativecosts of the most common operator splitting and implicitmethods for coupled diffusion and reaction systems. Wediscuss the practical application of recently developed sta-bility theory (Ropp & Shadid, 2005) on these systems andpoint out both advantages and disadvantages of split andimplicit strategies. This work was performed under theauspices of the U.S. Department of Energy by Universityof California Lawrence Livermore National Laboratory un-der Contract W-7405-Eng-48

Carol S. WoodwardLawrence Livermore Nat’l Labcswoodward@llnl.gov

Clint DawsonInstitute for Computational Engineering and SciencesUniversity of Texas at Austinclint@ices.utexas.edu

Jason HowellClemson UniversityDepartment of Mathematical Sciencesjshowel@math.clemson.edu

MS13

Moderator

Bruce HendricksonSandia National Labsbahendr@sandia.gov

MS14

Parallel AMG Setup Phase Algorithms

The performance of AMG depends heavily on the quality ofthe coarse grids and transfer operators constructed duringthe setup phase. New theory and setup phase algorithmshave been developed in recent years in an effort to makeAMG more robust. These algorithms are often inherentlysequential, and developing efficient, scalable algorithms inparallel remains a principle challenge. This talk focuseson recent algorithmic work on parallel coarse grid selectionand parallel transfer operator construction.

Luke OlsonDepartment of Computer ScienceUniversity of Illinois at Urbana-Champaignlukeo@uiuc.edu

David AlberDepartment of Computer ScienceUniversity of Illinois at Urbana-Champaignalber@uiuc.edu

MS14

Algebraic Multigrid Methods for Systems of PDEs

Modifications to classical AMG are required when solv-ing linear systems derived from systems of PDEs involvingmultiple unknowns. Two accepted approaches are treatingvariables corresponding to the same unknown separately(the ”unknown” approach) and treating variables corre-sponding to the same physical node together (the ”nodal”approach). We discuss the applicability and parallel per-formance of each approach as well as our investigation intoalternative interpolation and coarsening algorithms.

Allison H. BakerCenter For Applied Scientific ComputingLawrence Livermore National Laboratoryabaker@llnl.gov

Ulrike Meier YangCenter for Applied Scientific ComputingLawrence Livermore National Laboratoryumyang@llnl.gov

MS14

Parallel Auxiliary Space AMG for Maxwell Prob-lems

Recently, Hiptmair and Xu introduced a new auxil-iary space preconditioner for constant coefficient definiteMaxwell problems. We present numerical experiments witha parallel version of their method, which utilizes two inter-nal AMG V-cycles for scalar and vector Poisson-like matri-ces. Our tests include problems with variable coefficientsand zero conductivity, and clearly demonstrate the scala-bility of this preconditioner on hundreds of processors. Theimplementation is part of the hypre library and is based on

96 CS07 Abstracts

its algebraic multigrid solver BoomerAMG.

Tzanio V. Kolev, Panayot S. VassilevskiCenter for Applied Scientific ComputingLawrence Livermore National Laboratorytzanio@llnl.gov, panayot@llnl.gov

MS14

Long-Range Interpolation for Parallel AlgebraicMultigrid

Algebraic multigrid (AMG) is a very efficient algorithmfor solving sparse unstructured linear systems. However,for large three-dimensional problems, traditional coars-ening algorithms often generate growing complexities interms of memory use and computations per AMG V-cycle.The PMIS coarsening algorithm remedies this complexitygrowth, but leads to non-scalable AMG convergence factorswhen classical interpolation is used. We study the scalabil-ity of AMG methods that use PMIS coarsening combinedwith long-range interpolation methods for a variety of rel-evant test problems on parallel computers.

Hans De SterckUniversity of Waterloohdesterck@math.uwaterloo.ca

Ulrike Meier YangCenter for Applied Scientific ComputingLawrence Livermore National Laboratoryumyang@llnl.gov

Josh NoltingUniversity of Colorado at Boulderjosh.nolting@colorado.edu

MS15

Effects of Alcohols and Pore-Forming Peptides onLipid Bilayers

Lipid bilayers are important inhomogeneous fluid systemsthat mediate the interaction of cells with their environ-ment. We have applied a classical density functional theory(DFT) to a coarse-grained model of lipid and solvent, de-signed to self-assemble into a bilayer. We will present tworecent results: the effects of alcohols on the mechanicalproperties of lipid bilayers, and the structure and free en-ergy of pores formed in the bilayer by assemblies of modelpeptides.

Amalie FrischknechtSandia National Laboratoriestba@sandia.gov

Laura FrinkSandia National Labsljfrink@sandia.gov

MS15

Selectivity and Permeation of Ions in Biological IonChannels

Biological ion channels conduct ions across membranesdown chemical potential gradients. Some ion channels canselect which ion species they conduct, a property importantfor physiological function. The region of the pore wherethis selectivity occurs is usually highly-charged, especiallyin the case of Ca- and Na-selective channels. Density func-

tional theory of fluids coupled with drift-diffusion equationsreproduce and predict experimental channel data and isused to understand the physics of selectivity of channels.

Robert S. EisenbergDept. of Molecular BiophysicsRush University Medical Centerbeisenbe@rush.edu

Wolfgang NonnerRush University Medical Centertba@rush.edu

Dirk GillespieRush University Medical CenterDepartment of Molecular Biophysics & Physiologydirk gillespie@rush.edu

MS15

Osmotic Pressure and Packaging Structure ofCaged DNA

Packaging double-stranded (ds)DNA in a small viral capsidmust overcome strong electrostatic repulsion due to back-bone charges and the ultimate packing density is limitedby the free volume available to the colossal molecule. Mul-tiple length scales make it a formidable task to describe thestructure and thermodynamic properties caged DNA froma microscopic perspective. This work presents a theoreticalmodel for aqueous solutions of dsDNA. Predictions of thetheory are in good agreement with experiments.

Jianzhong WuUniversity of California, Riversidetba@email

MS16

Local Calculation of Conservative Edge Fluxesfrom Finite Element Hydrodynamic Models

A method for calculating conservative edge fluxes for afinite element hydrodynamic model is demonstrated for the2D shallow water equations. The method is local and reliesupon physically relevant parameters such as the nodal fluxand circulation. Requirements for using this approach arethat the finite element method is in conservative form andthe test functions sum to an elemental constant.

Jackie P. HallbergU.S. Army Corps of EngineersJackie.P.Hallberg@erdc.usace.army.mil

Charlie R. BergerU.S. Army ERDCCoastal & Hydraulics Laboratorycharlie.r.berger@erdc.usace.army.mil

MS16

Development of a Software Toolkit for Consistent-Conservative Flux Computation

Model coupling is a prosperous research field. Independentmeshes and different numerical methods commonly exist ineach component/model. Theoretically, globally and locallymass conservation has to be preserved when it is checkedconsistently, or even when the flux is computed inconsis-tently with the discrete equation being solved. This pa-per presents a software toolkit to provide coupling model

CS07 Abstracts 97

developers with capabilities for obtaining consistent andconservative flux computation without large investmentsof effort or time.

Jing-Ru Cheng

Major Shared Resource Center (MSRC)U.S. Army Engineer Research and Development Center(ERDC)Ruth.C.Cheng@erdc.usace.army.mil

Robert M. HunterU.S. Army Engineer Research & Development Centerrobert.m.hunter@erdc.usace.army.mil

MS16

A Local Conversion From Nodal Flow to Edge Flow

Mass-conservative nodal flow can be received by back sub-stituting the numerical solution into the discretized equa-tions of mass conservation with the finite element method.To compute flow through a desired cross section that iscomposed of a number of element edges, a local conver-sion from nodal flow to edge flow is proposed. A two-dimensional subsurface flow example is used to demon-strate this method and discuss its strengths and weak-nesses.

Jing-Ru ChengMajor Shared Resource Center (MSRC)U.S. Army Engineer Research and Development Center(ERDC)Ruth.C.Cheng@erdc.usace.army.mil

Hwai-Ping ChengUS Army Engineer Research & Development Centerhwai-ping.cheng@erdc.usace.army.mil

MS16

Locally Conservative Algorithms for Flow

When modeling fluid flow and transport problems, it is de-sirable to have locally conservative velocities on the trans-port grid. Lack of local mass conservation can result inspurious sources and sinks to the transport equation. Wedescribe several numerical locally conservative algorithms:discontinuous Galerkin, mixed finite element, and mimeticfinite difference methods. We also discuss a priori and aposteriori convergence results and compare advantages anddisadvantages of each of these methods with projection ap-proaches.

Mary F. WheelerCenter for Subsurface ModelingUniversity of Texas at Austinmfw@ticam.utexas.edu

MS17

Model Reduction Applied to Large-Scale Struc-tural Dynamics and Control

Structural vibration control continues to be an active topicof investigation. The application to highly complex large-scale systems can involve finite element discretizations withmillions of states and similarly large number of unknownparameters. The active control of these complex systemsposes many unsolved problems and daunting challenges. Akey challenge is designing practical controllers for activecontrol applications of complex structures. Modern con-

trol techniques yield controllers of order comparable thephysical system model, thus making real-time implemen-tation difficult and often impractical. Therefore generationof lower-dimensional models that closely approximate fullorder systems are desirable for the analysis and control oflarge-scale systems. In the literature, model reduction hasbeen studied both in control engineering and structuralanalysis. A very challenging large-scale control problemthat has emerged recently is the protection of civil struc-tures, such as high-rise buildings and long-span bridges,from dynamic loadings such as earthquakes, high wind,and heavy traffic. This presentation provides an overviewof model and controller reduction techniques applied tostructural dynamics problems in building control. A com-parative study is performed using Modal Reduction, GuyanReduction, Balanced Truncation and Krylov Techniques ina large-scale setting together with extensions to the closed-loop controller reduction problem.

Athanasios C. AntoulasDept. of Elec. and Comp. Eng.Rice Universityaca@rice.edu

Eduardo GildinInstitute for Computation Engineering and Sciences -CSMUT Austineglidin@mail.utexas.edu

Danny C. SorensenRice Universitysorensen@rice.edu

MS17

An Algebraic Krylov Substructuring for Model Or-der Reduction

Substructuring techniques are usually based on the super-position of the eigenmodes. In this talk, we present aKrylov mode based substructuring method, which is sim-ilar to the popular component mode synthesis technique;however, no eigenmodes of the interior substructures areevaluated. This new scheme replaces the eigenmodes ofinterior substructures by proper Krylov modes of the sub-structures, which take the force and the coupling amongsubstructures into account. The accuracy improvementsof this new scheme are demonstrated by numerical resultsfrom structural dynamics in both frequency and time do-mains.

Ben-Shan LiaoUC DavisDepartment of Mathematicsliao@math.ucdavis.edu

MS17

A Parallel Scheme for Solving Large-Scale Lya-punov Equations

We present a parallel preconditioned iterative scheme forsolving the large-scale Lyapunov equations that arise whenone attempts to obtain a reduced-order model of large-scalestructures subjected to strong ground motion. Numericalexperiments are presented to explore the effectiveness ofthis scheme compared to others, and to demonstrate itsperformance on parallel computing platforms.

Ahmed Sameh, Carl Mikkelsen

98 CS07 Abstracts

Department of Computer SciencePurdue Universitysameh@cs.purdue.edu, cmikkels@cs.purdue.edu

MS17

Advancing Analysis Capabilities with ANSYS

The CAD/CAE software environment has now become anaccepted tool in engineering design. In its most effectiveuse computer simulation is an integrated part of the designand manufacturing process from concept to production.This talk describes some major efforts at ANSYS that con-tinue to advance analysis capabilities. These major effortsinclude software innovation and initiatives to maximize thecapabilities of high performance computing. The ability tosolve complex assemblies with detailed models has beenadvanced to new levels by ANSYS breakthrough achieve-ments in parallel processing and large memory computing.This talk will describe current and future hardware devel-opments as well as algorithmic breakthroughs that havemade these achievements possible. Examples will be giventhat illustrate the current state-of-the art capabilities ofANSYS today and motivate the future goals for furtherdevelopments in the world of CAD/CAE software.

Gene PooleANSYS, Incgene.poole@ansys.com

MS18

Moderator

Phil ColellaLawrence Berkeley National Laboratorypcolella@lbl.gov

MS19

ELLAM for Resolving Kinematics of ResistiveMagnetohydrodynamic (MHD) Flows

The kinematics of MHD studies the influence of the veloc-ity of an electrically conducting fluid on the magnetic field,which conserves the solenoidal property for all time. Forthe 2-dim case, a scalar potential can be introduced andthe magnetic field induction equation can be converted intoa convection-diffusion-reaction equation, which can be effi-ciently solved by the Eulerian-Lagrangian localized adjointmethod (ELLAM). For the 3-dim case, locally divergence-free finite elements are used to satisfy the solenoidal prop-erty and the discontinuous Galerkin method comes intoplay very naturally. Simulations for some interesting MHDeddy flows will be presented, including analysis on distor-tion and energy evolution of magnetic fields. This is a jointwork with Hongsen Chen, Richard Ewing, Shuyu Sun, andSimon Tavener.

Jiangguo LiuColorado State Universityliu@math.colostate.edu

MS19

Data Assimilation into Some Wildfire Models

A wildfire is modeled by a system of nonlinear reaction-convection-diffusion equations. Solutions of such equationsexhibit traveling waves, which consist of a reaction zoneand a cool-down zone. The width of the reaction zone is less

than the modeling scale and thus modeling in the reactionsheet limit is also considered, which leads to fireline evo-lution and fire spread models. The wildfire model standsalone or it is coupled with an atmospheric model (weatherforecasting). Data is assimilated into a running model bya version of the Ensemble Kalman Filter (EnKF). Origi-nally, EnKFs attempt to fit the measurements by a leastsquares fit using linear combinations of ensemble members,and the ensemble is derived by adding perturbation to agiven initial state. This makes fitting thin reaction in-terfaces difficult. So, in addition to additive perturbationand correction, we use also spatial deformation, level-settechniques, and a new class predictor-corrector ensemblefilters. The predictor-corrector filters combine the ideas ofEnKF, empirical data assimilation such as nudging, andsequential Monte-Carlo methods. The predictor delivers aproposal ensemble that may not have the correct statis-tics, but it should be close the to analysis ensemble (i.e.,ensemble with new data incorporated). The corrector thenuses density estimation to assign weights to members ofthe proposal ensemble to obtain correct statistics.

Jan MandelUniversity of Colorado at DenverDepartment of Mathematical Sciencesjmandel@math.cudenver.edu

Jonathan D. BeezleyDepartment of Mathematical SciencesUniversity of Colorado at Denver and Health SciencesCenterjbeezley@math.cudenver.edu

Minjeong KimDepartment of Mathematical SciencesUniversity of Colorado at Denver and Health SciencesCentermkim@math.cudenver.edu

MS19

A-Posteriori Analysis of an Operator SplittingMethod for Heat Transfer Through a Fluid-SolidInterface

We consider operator decomposition methods to be a spe-cial form of operator splitting in which a real or artificialinterface provides a natural partition. For example, non-overlapping domain decomposition methods may be con-sidered as a type of operator decomposition. We presentan a-posteriori adjoint-based analysis of the stability andaccuracy of an operator decomposition method for a mul-tiphysics problem which involves the exchange of informa-tion across a physical boundary. We illustrate our approachwith a heat transfer problem in which a cool solid is em-bedded within a hot Newtonian fluid.

Donald EstepColorado State Universityestep@math.colostate.edu

Tim WildeyDepartment of MathematicsColorado State Universitywildey@math.colostate.edu

Simon TavenerColorado State Universitytavener@math.colostate.edu

CS07 Abstracts 99

MS19

A Computational Flow Simulation in MultiphysicsEnvironment

The aim of this talk is to introduce a coupled surface andsubsurface flow problem arising from flood prediction andcontrol. The mathematical and computational challengesare: (1) model deveoplement and model reduction, (2)numerical approximation for shallow water equation withcomplex physics, (3) algorithm design, (4) computer sim-ulation/implementation, and (5) validation. The first fourchallenges shall be discussed in this talk, and particularlyemphasis will be given to the model development and al-gorithm design. The talk should be accessible to generalaudience in applied/computational mathematics and hy-draulogy.

Junping WangNational Science Foundationjwang@nsf.gov

MS20

New Developments of Fast First Principles Com-putational Methods for Biochemical Simulations

Methods of directly simulating the behavior of complexstrongly interacting atomic systems (molecular dynamics,Monte Carlo) have provided important insight into thebehavior of many biochemical systems such as DNA, en-zymes, and membranes. The limitation of the even widerapplication of these methods is the difficulty of developingrepresentations of potential interactions in these systemsat the molecular level that capture their complex chem-istry that is commonly encountered in these systems (reac-tions, polarization, etc.). Static quantum chemistry meth-ods have provided a means to calculate reactive mecha-nisms in cluster approximations to mineral systems. Thesemethods are limited to small atomic sizes and generallycannot be applied to problems in which dynamics play arole. In this talk new developments in the implementa-tions of methods to simultaneously simulate the electronicstructure and molecular dynamics of nanoscale materialswill be described (ab-initio molecular dynamics, AIMD).These methods have at their core the calculation of inter-atomic forces from the fast iterative solution of the den-sity functional approximation to the electronic Schrdingerequation and, therefore, avoid problems of force develop-ment limiting the application of MD. They are designed toefficiently provide the DFT solutions to problems of verylarge size and so generalized the application of quantumchemistry to very large system while at the same time re-moving the limitation of quantum chemistry methods tostatic systems. This talk will focus on the development inthree areas: the implementation a local basis/plane wavemethod (projector augmented plane-wave method, PAW)that removes the use of pseudopotentials, the developmentof a plane wave implementation of exact exchange, and thedevelopment of an adaptive multilevel finite element firstprinciples solver. The talk will focus on the fundamentalsof these methods and the realities in terms of system size,computational requirements and simulation times that arerequired for their application.

Eric J. BylaskaFundemental Sciences LaboratoryPacific Northwest National Laboratoryeric.bylaska@pnl.gov

Marat ValievEnvironmental Molecular Systems Laboratory

Pacific Northwest National Laboratorymarat.valiev@pnl.gov

Mike HolstDepartment of MathUCSDmholst@math.ucsd.edu

John WeareDepartment of ChemistryUCSDjweare@ucsd.edu

MS20

Simulation of Diffusion Tensor Imaging (DTI) inRealistic Neural Tissues

MRI measurement of diffusion in realistic neural tissuesmodels has many complexities. By using Monte Carlo sim-ulation environment MCELL with computational modelsof neural tissues, we developed a computational environ-ment that simulates the signal in diffusion weighted MRIexperiments in neural tissues, including the influence oftissue geometry and pulse sequence parameters. Allowingfor the assessment of physiological parameters on the MRDWI signal, the efficacy of data analysis techniques, andthe optimality of pulse sequence parameters.

Lawrence FrankUCSD: Department of Radiology & Center for FunctionalMRIUniversity of California, San Diegolfrank@ucsd.edu

MS20

Chemical Transformations in Complex BiologicalSystems: Hybrid Quantum Mechanical and Molec-ular Mechanics Methodologies

Accurate description of chemical transformations in com-plex biological systems remains one of great challenges incomputational biology. This problem is inherently multi-scale and requires efficient integration of several levels oftheory to bridge fine description of the electronic structureeffects with large scale dynamical fluctuations of the sur-rounding protein environment. One particular methodol-ogy that was found successful in describing problems of thistype is based on combined quantum mechanical and molec-ular mechanical (QM/MM) methodologies. The focus ofthis talk will be to give a general overview of QM/MMmethods, as well and discuss latest developments and chal-lenges in this field. As a particular application exampleDNA photostability problem will be considered.

Marat ValievEnvironmental Molecular Systems LaboratoryPacific Northwest National Laboratorymarat.valiev@pnl.gov

MS20

Large Scale First Principles Simulations of Signal-ing Phosphoryl Transfer Reactions

A major limitation to simulating reactive biochemical pro-cesses is the development of accurate representations ofthe many-body forces that lead to their interesting proper-ties, while retaining large enough particle numbers in thesimulation to correctly describe their chemistry. Recently

100 CS07 Abstracts

progress has been made in the development of simulationmethods for very large systems based on forces calculateddirectly from the electronic Schrdinger equation. In or-der to carry out these calculations is necessary to solve avery large nonlinear eigenvalue problem on the fly. Thesemethods combine the essential features of high level quan-tum chemistry with those molecular dynamics to producea 1st principles based parameter free method of simula-tion. While they are leading to new insights into biochem-ical problems, there are significant numerical limitations totheir application. In this talk these problems will be dis-cussed in the context of our recent calculations on the ki-nase reaction mechanism. The kinase enzymes catalyze themost important signaling events in eukaryote cells. Theycatalyze the transfer of the -phosphoryl group of ATP toserine, threonine, and tyrosine residues in proteins. Evenafter careful structural characterization and many years ofstudy the mechanism of the phosphoryl transfer reactionin these systems is still poorly understood. In this projectwe use a combined quantum mechanical and molecular me-chanics approach (QM/MM) to analyze the mechanism ofthe phosphorylation reaction in a well characterized mem-ber of the kinase family – cAMP dependent serine pro-tein kinase (cAPK). In order to obtain reliable results wehad to include roughly 150 atoms in a full B3LYP cal-culation coupled with an additional 54,000 molecular me-chanics atoms representing the protein environment. Ourcalculations support a dissociative mechanism for the reac-tion process with a late proton transfer to a catalytic baseresidue. This mechanism is consistent with observations.

John WeareDepartment of Chemistry and BiochemistryUniversity of California, San Diegojqw@ucsd.edu

Eric J. BylaskaFundemental Sciences LaboratoryPacific Northwest National Laboratoryeric.bylaska@pnl.gov

Marat ValievEnvironmental Molecular Systems LaboratoryPacific Northwest National Laboratorymarat.valiev@pnl.gov

MS21

Domain-Decomposition and Operator-Split Smoothers forInverse Problems with Parabolic PDEs

Parabolic PDEs model physical systems in science and en-gineering. We are interested in devising efficient numer-ical schemes for inverse and control problems related tosuch systems. In this talk we present results for the linearheat equation with a non-constant coefficient reaction-liketerm. First we discuss space-time smoothers for the for-ward problem. We propose a new smoother, inspired byoperator-splitting methods, which can be combined withdomain decomposition. Second we discuss the spectralproperties of the inverse operator (reduced Hessian) anddiscuss smoothers. The basic single level techniques are theKing-Kaltenbacher class preconditioners, Borzi pointwisesmoothers, and space-time domain decomposition tech-niques. We conclude with analysis of complexity and con-vergence rates, their effectiveness when used in a full multi-grid scheme, verify the analysis with numerical results, andcompare them with the proposed smoothers.

Santi Swaroop Adavani, George Biros

University of Pennsylvaniaadavani@seas.upenn.edu, biros@seas.upenn.edu

MS21

Mesh Adaptivity for Inverse Problems

The numerical solution of inverse problems governed byPDEs is often challenging, since it involves the discretiza-tion of both a state variable and the unknown parameter(for example material properties). In adaptive schemes,they should be discretized on separate meshes. This, andthe saddle point structure of the problem, makes the con-struction of efficient solvers such as multigrid difficult. Wepresent a scheme for independent discretization and effi-cient solution, and point out challenges to this approach.

Wolfgang BangerthTexas A&M Universitybangerth@math.tamu.edu

MS21

Multilevel Methods in Image Registration

Abstract not available at time of publication.

Eldad HaberEmory UniversityDept of Math and CShaber@mathcs.emory.edu

MS21

Model Problems in PDE-Constrained Optimiza-tion

We hope to aid in benchmarking algorithms for PDE-constrained optimization problems by presenting a set ofsuch model problems. We specifically examine a type ofPDE-constrained optimization problem, the parameter es-timation problem. We present three model parameter esti-mation problems, each containing a different type of partialdifferential equation in the constraint. We also describe dif-ferent discretization and solution techniques for each prob-lem, presenting numerical results to compare such tech-niques.

Lauren HansonEmory Universitylrhanso@emory.edu

Eldad HaberEmory UniversityDept of Math and CShaber@mathcs.emory.edu

MS22

Images: New Perspectives in Data Assimilation

Assimilation of satellite images is an attempt to conjugatethe information contained in atmospheric or oceanographicmodels and images. We will discuss the main directions ofresearch in this field. The first approach is to estimatefrom images some pseudo observations such as velocitiesthen to assimilate them in a classical scheme of data as-similation. The other approach is to add to the classicalvariational analysis a space of images with a metric struc-ture and an operator from the space of the solutions ofthe numerical model toward the space of images in orderto be able to compute the discrepancy between the model

CS07 Abstracts 101

and the images then to plug it in a variational method. Inthis communication we will present both approaches withapplications to actual situations, the comparison betweenthese approaches will be discussed.

Francois-Xavier Le DimetUniversite Joseph Fourier and INRIAledimet@imag.fr

MS22

Localized Ensemble Kalman Data Assimilation forAtmospheric Chemical Transport Models

The task of providing an optimal analysis of the state ofthe atmosphere requires the development of dynamic data-driven systems that efficiently integrate the observationaldata and the models. In this paper we discuss practicalaspects of nonlinear ensemble data assimilation applied toatmospheric chemical transport models. We highlight thechallenges encountered in this approach such as filter di-vergence and spurious corrections, and propose solutionsto overcome them, such as background covariance inflationand filter localization. The predictability is further im-proved by including model parameters in the assimilationprocess. Results for a large scale simulation of air pollu-tion in North-East United States illustrate the potential ofnonlinear ensemble techniques to assimilate chemical ob-servations.

Adrian SanduVirginia Polytechnic Instituteand State Universityasandu@cs.vt.edu

MS22

The Inverse Ocean Model: A Toolkit for CreatingGeophysical Data-Assimilation Systems

The Inverse Ocean Model system is a modular soft-ware package that implements Weak-constraint, Four-Dimensional Variational (W4DVAR) assimilation for anydynamical model and observing array, both of which maybe nonlinear but functionally smooth. Program templates,coded in Parametric Fortran, enable custom code genera-tion for user’s models, which have included primitive equa-tions and shallow water models on structured and unstruc-tured grids, with numerics ranging from finite-differencesto spectral elements.

Edward ZaronDepartment of Civil and Environmental EngineeringPortland State Universityzaron@cee.pdx.edu

MS22

Issues in Ensemble Assimilation/Prediction for Ex-treme Events

By definition, the extreme values belong to the tails of aprobability distribution function (PDF). The consequenceof using a typical Gaussian framework is that the extremeevent observations will be rejected, or given a negligibleweight, thus discarding the important new information.We will discuss challenging issues and present a maximumlikelihood ensemble methodology designed to assimilate ex-treme value observations, based on the use of mixed Gaus-sian and Extreme Value PDFs.

Milija Zupanski

Cooperative Institute for Research in the AtmosphereColorado State UniversityZupanskiM@cira.colostate.edu

MS23

NOMADm: A MATLAB Software Package forSurrogate-Based Black Box Optimization

In this talk, we discuss the implementation of both inter-polatory and simplified physics surrogates as an aid in nu-merically solving nonlinear and mixed variable optimiza-tion problems, in which objective and constraint functionsare computationally expensive and derivatives are gener-ally not available. The NOMADm software package is aMATLAB code based on the class of mesh adaptive directsearch (MADS) algorithms for derivative-free optimization.The flexibility of the search step in MADS allows for theconstruction and optimization of less expensive surrogatefunctions. The talk focuses on different types of surrogates,strategies for using surrogates on mixed variable prob-lems (especially when nonnumeric categorical variables arepresent), simplified physics surrogates, and additive surro-gates that make use of both interpolation and simplifiedphysics models. A few applications will be discussed.

John Dennis, Jr.Rice Universitydennis@rice.edu

Arantzazu Garci Garcia LekueDonostia International Physics Center (DIPC), Donostia,Spaiwmbgalea@lg.ehu.es

Mark AbramsonAFITmark.abramson@afit.edu

Juan C. MezaLawrence Berkeley National LaboratoryJCMeza@lbl.gov

MS23

Formulations for Surrogate-Based OptimizationUsing Data Fit and Multifidelity Models

Surrogate-based optimization (SBO) methods have becomeestablished as effective techniques for engineering designproblems through their ability to tame nonsmoothness andreduce computational expense. Possible surrogate mod-eling techniques include data fits (local, multipoint, orglobal), multifidelity model hierarchies, and reduced-ordermodels, and each of these types has unique features whenemployed within SBO. We discuss a number of SBO algo-rithmic variations and their effect for each of the surrogatemodeling cases. First, general facilities for constraint man-agement will be explored through approximate subproblemformulations (e.g., direct surrogate), constraint relaxationtechniques (e.g., homotopy), merit function selections (e.g.,augmented Lagrangian), and iterate acceptance logic selec-tions (e.g., filter methods). Second, techniques specializedto particular surrogate types will be described. Compu-tational results will be presented for a selected set of testproblems using the DAKOTA software.

Danny DunlavyOptimization and Uncertainty Estimation DepartmentSandia National Laboratoriesdmdunla@sandia.gov

102 CS07 Abstracts

Michael S. EldredSandia National LaboratoriesOptimization and Uncertainty Estimation Dept.mseldre@sandia.gov

MS23

Generation of Optimal Artificial Neural NetworksUsing a Pattern Search Algorithm: Application toApproximation of Chemical Systems

A pattern search optimization method is applied to thegeneration of optimal artificial neural networks (ANNs).Optimization is performed using a mixed variable extensionto the generalized pattern search method. When used witha surrogate, the resulting algorithm is highly efficient forexpensive objective functions. Results of this approach ap-plied to a chemistry approximation problem demonstratethe effectiveness of this method.

Alison MarsdenStanford UniversityMechanical Engineering Dept.amarsden@stanford.edu

Matthias IhmeStanford UniversityMechanical Engineeringmihme@stanford.edu

Heinz PitschCITSStanford UniversityH.Pitsch@stanford.edu

MS23

Derivative-Free Trust-Region Methods Using Ra-dial Basis Functions

We implement a derivative-free trust-region optimizationmethod using different types of radial basis function (RBF)models. We compare the performance of these Trust-Region RBF algorithms to alternative local optimizationmethods, including Newuoa, Pattern Search, and a Quasi-Newton method, on a variety of test problems. Wealso compare these algorithms on two environmental ap-plications, namely, groundwater bioremediation and thecalibration of a watershed model. The results indicatethat the Trust-Region RBF approach is very promising inderivative-free optimization. Finally, we will explore someparallelization strategies for Trust Region RBF algorithms.

Rommel G. RegisCornell Theory Center, Cornell Universityrgr6@cornell.edu

Stefan M. WildCornell UniversitySchool of Operations Research & IEsmw58@cornell.edu

Christine ShoemakerCornell Universitycas12@cornell.edu

MS24

Computational Science PhD at San Diego State

University

San Diego State University (SDSU) offers a doctoral degreein computational science, the first in California, in collabo-ration with Claremont Graduate University (CGU), Clare-mont, CA. the program involves graduate level courses andresearch projects under the supervision of SDSU facultyfrom the departments of engineering, physics, mathemat-ics, computer science, chemistry, and biology with coop-erating faculty from CGU. the ph.d. degree is awardedjointly by the two institutions. We will describe the pro-gram curriculum and highlite some of the research projects.

Jose CastilloSan Diego State UniversityComputational Science Researchcastillo@myth.sdsu.edu

MS24

The Growing Role of the TeraGrid in the Compu-tational Science Education Pipeline

The NSF-funded TeraGrid is the worlds first large-scaleand production grid infrastructure for open scientific re-search. The San Diego Supercomputer Center (SDSC)serves as the data-intensive site lead for the TeraGrid.SDSC has a vested interest in the computational scienceeducation pipeline not only as a user of computational sci-ence resources but also as a potential future employer ofstudents currently interested in computational science andengineering. In response to an NSF mandate that usersfrom HPC Expert to K-12 student should benefit fromthe TeraGrid, TeraGrid partners are developing a seriesof Gateways. TeraGrid Gateways are web-based portalsconsisting of front-end grid services that provide teragrid-deployed applications used by a discipline-specific commu-nity. Gateways are intended to: streamline the processof doing research that depends on high-performance com-puting, reach a broader community of users, and helpdefine the specifications for a computational science edu-cation pipeline, An important long-term goal of TeraGridGateways is to engage communities that are not tradi-tional users of the supercomputing centers by providingcommunity-tailored access to TeraGrid services and ca-pabilities so they may take advantage of existing com-munity investment in software, services, education, andother components of Cyberinfrastructure. Ten Gatewaysare currently under development in a diverse range ofdisciplines including nanotechnology, atmospheric science,bioinformatics, and traffic flow. Gateways feature workflowmanagement tools and expert technical support to maxi-mize productivity. The Grid Computing Environments Re-search Group solicits and analyzes Gateway user feedbackto help improve the interface and respond to user needs.Teragrid partners or Resource Providers offer workshops,institutes, seminars and provide on-line learning resourcesto support and promote the effective use of TeraGrid re-sources.

Jeff SaleEducation DivisionSan Diego Supercomputer Centerjsale@sdsc.edu

MS24

3d Game Programming as a CS Service-LearningCurriculum for High School Science Courses

3d computer games are undeniably popular today and

CS07 Abstracts 103

many university Computer Science (CS) majors are ea-ger to gain skills at programming their own game. Wehave been able to capitalize on this interest to develop acourse where students learn to code effective games us-ing the Torque 3d Game Engine from garagegames.com.This course requires appropriate CS content to understandthe 3d environment and the Object Oriented Scripting lan-guage. The course goal is to collaborate with an educatorwho can pose the 3d topic to be explored. With the ac-cepted high school science standards, this module can becharacterized and can be useful to a large wide body of highschool science teachers. Since current high school studentsare of a generation that was born digital, they are comfort-able and engaged when exploring topics delivered withinthe game environment. This scientific visualization appli-cation can be further applied to topics in computationalscience.

Kris StewartSan Diego State UniversityDept of Computer Sciencestewart@cs.sdsu.edu

MS24

Undergraduate Computational Science Curricula:Programs and Educational Materials

There is a growing number of undergraduate CSE curric-ula. This presentation will first highlight the different ver-sions of computational science programs (e.g., B.Sc. pro-grams, minor programs, certificate programs, etc) that de-pend on the type of institution and local resources. Wewill also present a model curriculum and provide specificexamples of educational materials developed by the KeckUndergraduate Computational Science Education Consor-tium.

Ignatios E. VakalisProfessor of Computer ScienceCalPoly State Univ. San Luis Obispoivakalis@csc.calpoly.edu

MS25

The Entrainment and Optimal Control of Circa-dian Phase Dynamics

Circadian rhythms are observed at all cellular levels affect-ing cell function, division, and growth. These approximatetimekeepers synchronize organisms to the environment andto one another through entrainment factors such as light.An inability to entrain the biological clock leads to a vari-ety of circadian-related disorders. Our objective is to bet-ter understand and control circadian entrainment throughdevelopment and application of a closed-loop model pre-dictive control algorithm, where light serves as the manip-ulated control input.

Neda BagheriUniversity of California, Santa BarbaraDept. of Electrical and Computer Engineeringneda@ece.ucsb.edu

MS25

A Molecular Model for Intercellular Synchroniza-tion in the Mammalian Circadian Clock

Abstract not available at time of publication.

Frank Doyle

University of California, SantDepartment of Chemical Engineedoyle@engineering.ucsb.edu

Michael HensonUniversity of MassachusettsDepartment of Chemical Engineeringhenson@ecs.umass.edu

MS25

Period Determination Among Circadian Pacemak-ers

Abstract not available at time of publication.

Erik HerzogDepartment of BiologyWashington Universityherzog@wustl.edu

MS25

BioSens: A Sensitivity Analysis Toolkit for Sys-tems Biology

Sensitivity analysis guides the development of ordinary dif-ferential equation models of biological systems. The sen-sitivity of characteristic behaviors to parametric perturba-tion identifies areas requiring refinement. For many oscil-latory systems, such as the circadian clock, phase behavioris the feature that best elucidates clock performance and,therefore, is the key behavior to analyze. We discuss periodand phase sensitivity for oscillatory systems and BioSens,a software toolkit for general systems.

Stephanie TaylorUniversity of California, Santa BarbaraDepartment of Computer Sciencestaylor@engineering.ucsb.edu

MS26

Direct and Inverse Algorithms for Stochastic Mod-els of Microrheology

The field of microrheology exploits experimental track-ing of micron-scale beads suspended in viscoelastic ma-terials to infer properties of the material. Passive mi-crorheology is based on entropic bead fluctuations, thefluctuation-dissipation theorem, and a generalized Stokes-Einstein drag law to deduce frequency-dependent storageand loss moduli of the material. Since the 1995 PRL ofT. Mason and D. Weitz, this method or variants of it havebeen applied as an alternative to bulk methods, or in bi-ology, to soft matter materials for which very small vol-umes are available. In addition to the standard applica-tion as an inverse characterization method, we are inter-ested in direct simulations of pathogens in pulmonary flu-ids. The lecture will highlight direct and inverse methodsand algorithms developed in our group based on gener-alized Langevin equation models and the statistical toolsof maximum likelihood estimators from noisy time seriesdata.

Tim ElstonUniversity of North CarolinaDepartment of Pharmacologytelston@email.unc.edu

Lingxing Yao, Christel Hohenegger

104 CS07 Abstracts

University of North CarolinaDepartment of Mathematicsyaol@amath.unc.edu, choheneg@email.unc.edu

John FricksDept of StatisticsPenn State Universityfricks@stat.psu.edu

M. G. ForestUNCforest@amath.unc.edu

MS26

Implicit Solvent Models: Level-Set Relaxation andGeneralized Born Approximations

Understanding biomolecules and their interaction with sol-vent such as water is essential to revealing mechanisms andfunctions of biological systems. While atomistic simula-tions that treat both solvent and solute molecules explicitlyare accurate, the recently developed implicit solvent mod-els for biomolecules greatly reduce the degree of freedomin simulations. In this talk, I will first introduce a class ofvariational implicit solvent models for biomolecules. I willthen present my recent work, jointly with L.-T. Cheng, J.Dzubiella, and J. A. McCammon, on level-set calculationsof equilibrium solvent-solute interface and free-energy fornonpolar solvation systems. Finally, I will introduce gen-eralized Born models for the electrostatics calculations inimplicit solvent models; and examine the validity of variousformulas of generalized Born radii.

Bo LiDepartment of Mathematics, UC San Diegobli@math.ucsd.edu

MS26

Continuum-Discrete Computation of ViscoelasticFlows

Abstract not available at time of publication.

Sorin M. MitranDept. of Mathematics, Applied Math Prog.University of North Carolinamitran@amath.unc.edu

MS26

Applications of An Energetic Variational Phase-Field Method for Numerical Simulation of Multi-phase Flows

Abstract not available at time of publication.

Jie ShenDepartment of MathematicsPurdue Universityshen@math.purdue.edu

MS27

Error Representation and Estimation in Compress-ible MHD

Error representation and estimation of numerically approx-imated functionals arising in time dependent compressiblemagnetohydrodynamics (MHD) is considered. The dis-

crete MHD stability theory [Barth, “On the Role of Involu-tions in Discontinuous Galerkin Discretization of Maxwelland MHD Systems”, IMA Volume on Compatible SpatialDiscretizations, Vol. 195, 2006] motivates several hybridFEM discretizations strategies for compressible MHD de-pending on

• strong or weak satisfaction of div B = 0 in elementinteriors

• strong or weak satisfaction of [B ·n]+− = 0 on elementinterfaces

where B denotes the magnetic induction field in MHD. Wethen consider the representation and estimation of errors incomputed MHD functionals for these discretizations usingerror estimation techniques developed by Becker and Ran-nacher [Becker and Rannacher, “Weighted A-Posteriori Er-ror Control in FE Methods”, Proc. ENUMATH-97, Hei-delberg, 1998]. A critical comparison of the various dis-cretization methods and error representation formulas re-veals rather significant differences in computational costand ease of implementation which are verified via numeri-cal experiments.

Timothy J. BarthNASA Ames Research CenterTimothy.J.Barth@nasa.gov

MS27

Coupled a Posteriori Error Estimation and Un-certainty Quantification for a Nonlinear ElasticityMEMS Problem

Quantification of both numerical error and probabilis-tic uncertainties is important for proper design of micro-electro-mechanical systems (MEMS). We present a goal-oriented a posteriori error estimator for the average sur-face force in a nonlinear elasticity problem that models aMEMS device. Our results demonstrate the performanceof the error estimator for both stand-alone deterministicmodels and for models that are embedded in calculationsfor uncertainty quantification and reliability-based designoptimization.

Brian M. AdamsSandia National LaboratoriesOptimization/Uncertainty Estimationbriadam@sandia.gov

Kevin Copps, Brian Carnes, Jonathan WittwerSandia National Laboratorieskdcopps@sandia.gov, bcarnes@sandia.gov,jwwittw@sandia.gov

Michael S. EldredSandia National LaboratoriesOptimization and Uncertainty Estimation Dept.mseldre@sandia.gov

MS27

Error Estimation and Adaptivity Tools for Nonlin-ear Thermal Applications

We discuss tools for error estimation and adaptivity basedon least squares recovery, element residual indicators, andadjoint-based estimators for local quantities of interest. Weexamine the practical implementation of these tools in aproduction parallel finite element code that approximatessolutions of nonlinear elliptic and parabolic equations. Wepresent results for transient heat conduction with contact

CS07 Abstracts 105

and enclosure radiation. The use of these tools is discussedin the wider context of code and solution verification.

Kevin D. Copps, Brian Carnes, David Neckels,Christopher K. NewmanSandia National Laboratorieskdcopps@sandia.gov, bcarnes@sandia.gov,dcnecke@sandia.gov, cnewman@sandia.gov

MS27

Adaptive Anisotropic Meshing Control for Cardio-vascular Flow Modeling

Many physical problems exhibit strong phenomena thatintroduce a need for anisotropic meshes. In viscous flowsimulations better results for key quantities of interest inregions of boundary layers can be obtained with a semi-structured boundary layer mesh. We will present an adap-tive procedure that adapts a boundary layer mesh to ananisotropic mesh size field defined such that the structureof the boundary layer mesh is maintained.

Onkar SahniRensselaer PolytechnicScientific Computation Research Centerosahni@scorec.rpi.edu

Kenneth Jansen, Mark S. ShephardRensselaer Polytechnic InstituteScientific Computation Research Centerkjansen@scorec.rpi.edu, shephard@scorec.rpi.edu

MS28

Experimental Data Visualization: Some Alterna-tives to Equal-Width Binning

We report on a set of adaptive-multiresolution binning ap-proaches, specially designed for data visualization in ex-perimental sciences where counting statistics follow poissondistributions. Fields of possible applications of algorithmshere described stem from astrophysics to condensed mat-ter sciences. Our main focus of interest concerns neutronspectroscopy data from single crystal samples where sig-nals span a fourdimensional space comprised by three spa-tial plus time dimensions. This makes a priori equal widthbinning schemes inadequate since physically relevant infor-mation is often concentrated within rather small regions ofsuch a space. Our aim is to generate optimally-binned datasets from 1D to 3D volumes to enhance the experimentersability to carry out searches within a 4D space. Several bin-ning algorithms are then scrutinized against experimentalas well as simulated data.

Francisco Bermejo, German BordelUniversity of the Basque Country, Spainjavier@langran.iem.csic.es, german@we.lc.ehu.es

Toby PerringRutherford Appleton Laboratory, United Kingdomtgperring@rl.ac.uk

Ibon BustinduyInstituto de Estructura de la MateriaSpanish Higher Research Council, Spainibon@langran.iem.csic.es

MS28

Adaptive Methods for PDEs and Conforming Cen-

troidal Voronoi Delaunay Triangulations

In this talk, we will discuss a new mesh adaptivity algo-rithm for elliptic PDEs that combines a posteriori errorestimation with centroidal Voronoi/Delaunay tessellationsof domains in two dimensions. The ability of the first ingre-dient to detect local regions of large error and the abilityof the second ingredient to generate superior unstructuredgrids result in an mesh adaptivity algorithm that has sev-eral very desirable features, including the following. Errorsare very well equidistributed over the triangles; at all levelsof refinement, the triangles remain very well shaped, evenif the grid size at any particular refinement level, whenviewed globally, varies by several orders of magnitude; andthe convergence rates achieved are the best obtainable us-ing piecewise linear elements.

Weidong ZhaoShandong University, Chinawdzhao@math.sdu.edu.cn

Max GunzburgerFlorida State UniversitySchool for Computational Sciencesgunzburg@scs.fsu.edu

Lili JuUniversity of South CarolinaDepartment of Mathematicsju@math.sc.edu

MS28

Reduced Order Modeling of Partial DifferentialEquations Via CVT

A reduced-basis method based on centroidal Voronoi tes-sellations (CVTs) is introduced. A discussion of reduced-ordering modeling for partial differential equations is givento provide a context for the application of reduced-orderbases. Then, detailed descriptions of CVT-based reduced-order bases including their construction from snapshot setstheir application to the low-cost simulation of partial dif-ferential equations and its control problems are given. Anadaptive method using density functions will also be intro-duced.

Hyung-Chun LeeAjou University, Koreahclee@ajou.ac.kr

John BurkardtSchool of Computational ScienceFlorida State Universityburkardt@scs.fsu.edu

Max GunzburgerFlorida State UniversitySchool for Computational Sciencesgunzburg@scs.fsu.edu

MS28

Radially Projected Finite Elements

We develop and analyze finite element discretizations fordomains with spherical geometry. In particular, we de-scribe the method used to approximate solutions (as wellas eigenvalues and eigenvectors) of partial differential equa-tions posed on the sphere, ellipsoidal shell,and cylindri-cal shell. These novel, so-called, ”radially projected finite

106 CS07 Abstracts

elements” are particularly attractive for numerical simu-lations since the resulting finite element discretization is”logically rectangular” and may be easily implemented inexisting finite element codes.

Necibe TuncerDepartment of Mathematics and StatisticsAuburn Universitytuncene@auburn.edu

Amnon MeirAuburn Universityajm@math.auburn.edu

MS29

Use of a Manufactured Solution for Verifying CFDFlux Schemes and BCs

Order-of-accuracy verification is necessary to ensure thatsoftware correctly solves a given set of equations. Onemethod for verifying the order of accuracy of a code isthe method of manufactured solutions. A manufacturedsolution is presented and deomonstrated that allows verifi-cation of not only the Euler, Navier-Stokes, and Reynolds-Averaged Navier-Stokes equation sets, but also some oftheir associated boundary conditions: slip, no-slip (adia-batic and isothermal), and outflow (subsonic, supersonic,and mixed).

Ryan B. BondSandia National LaboratoriesAerosciences Departmentrbbond@sandia.gov

Curtis C. Ober, Thomas M. Smith, Steven W. BovaSandia National LaboratoriesAlbuquerque, NMccober@sandia.gov, tmsmith@sandia.gov,swbova@sandia.gov

MS29

Verification of Overflow 2.0 through the Method ofManufactured Solutions

The overset grid code, OVERFLOW2.0y, is subject to ver-ification via the method of manufactured solutions (MMS).In this investigation, a prescribed, time-and-space-varyingsolution is inserted into the governing equations using sym-bolic software. The analytic remainder is then used as aforcing term within the numerical algorithm to be verified.Through successive space and/or time refinement, the so-lution error, produced via comparison to the prescribedsolution, may then verify the theoretical order-of-accuracyof a given discretization.

Paul CastellucciLawrence Livermore Nat’l Labpjcastel@llnl.gov

MS29

An Extreme Accuracy Benchmark via ConvergenceAcceleration for the McCormack Model for BinaryGas Mixture Channel Flow

Verification of computational algorithms for internal chan-nel flow of rarefied gases is an essential ingredient of re-liable code development. The analytical discrete ordi-nates (ADO) method has recently emerged as an efficient

algorithm to generate highly accurate numerical bench-mark solutions for a variety of internal flows of binarymixtures including Poiseuille, thermal-creep and diffusionflows. While the ADO method is computationally fast, itsimplementation may not be readily accessible to those whoare not transport aficionados. For this reason, this presen-tation will address the question, Can a simpler, more fun-damental, transport algorithm provide benchmarks com-parable to the ADO method for internal gas flow?

Barry GanapolDepartment of Aerospace and Mechanical EngineeringUniversity of Arizonaganapol@cowboy.ame.arizona.edu

MS29

Overview of Scientific Code Verification

Computer simulations have been increasingly contributingto the understanding of physical processes, analysis, anddesign of engineering systems. Terminology such as virtualprototyping and testing is being used in the developmentof engineering systems. Users of computational simulationtools face a critical question as how to evaluate the confi-dence in simulations. Verification, Validation, and Uncer-tainty Quantification are the primary tools to establish andquantify this confidence. An overview of scientific code ver-ification will be presented. This work was performed underthe auspices of the U. S. Department of Energy by Univer-sity of California Lawrence Livermore National Laboratoryunder Contract W-7405-Eng-48.

Kambiz SalariLawrence Livermore Nat’l LabCASCsalari@llnl.gov

MS30

How Scalable is Your Load Balancer?

Load-balancing (also known as partitioning) is a criti-cal component in parallel scientific computing to achievehigher degree of parallelism. The goal is to assign computa-tion to processors evenly while trying to minimize the com-munication volume. Graph and hypergraph partitioninghave served as useful approaches for this purpose over thelast decade. In this talk, we will discuss and present scal-ability performance of the state-of-the-art parallel graphand hypergraph partitioning tools.

Umit V. CatalyurekThe Ohio State UniversityDepartment of Biomedical Informaticsumit@bmi.osu.edu

Doru BozdagDepartment of Electrical & Computer EngineeringThe Ohio State Universitybozdagd@ece.osu.edu

Erik G. BomanSandia National Labs, NMDiscrete Math and Algorithmsegboman@sandia.gov

Karen D. DevineSandia National Laboratorieskddevin@sandia.gov

CS07 Abstracts 107

MS30

Parallel Hypergraph Repartitioning and Load Bal-ancing

Hypergraph partitioning is highly effective for many sci-entific applications. Its accurate communication modelenables higher quality than graph partitioning. Hyper-graphs also represent greater varieties of data, includingnon-square, non-symmetric data. Adaptive computations,however, require periodic repartitioning; hypergraph par-titioning can incur significant costs for data migration.We present parallel hypergraph repartitioners that accountfor existing partition assignments in computing new par-titions, thus reducing migration costs. We compare ourrepartitioners with both hypergraph partitioners and graphrepartitioners.

Doruk BozdagOhio State Universitybozdagd@ece.osu.edu

Lee Ann FiskSandia National Laboratorieslafisk@sandia.gov

Umit V. CatalyurekThe Ohio State UniversityDepartment of Biomedical Informaticsumit@bmi.osu.edu

Robert HeaphySandia National Laboratoriesrheaphy@sandia.gov

Erik G. BomanSandia National Labs, NMDiscrete Math and Algorithmsegboman@sandia.gov

Karen D. DevineSandia National Laboratorieskddevin@sandia.gov

MS30

Performance Improvement in a Mesh Quality Op-timization Application

We describe the use of combinatorial algorithms and re-lated techniques to improve the performance of a Newton-based mesh quality improvement application. We empha-size the use of runtime reordering transformations to im-prove data locality and the use of graph algorithms in au-tomatic differentiation to reduce the cost of gradient andHessian evaluations.

Sanjukta BhowmickDepartment of Applied Physics and Applied MathematicsColumbia Universitybhowmick@cse.psu.edu

Paul D. HovlandArgonne National LaboratoryMCS Division, 221/C236hovland@mcs.anl.gov

Todd S. MunsonArgonne National LaboratoryMathematics and Computer Science Divisiontmunson@mcs.anl.gov

Michelle StroutComputer Science Department,Colorado State Universitymstrout@cs.colostate.edu

MS30

Graph Coloring Problems for Computing Deriva-tives: Recent Developments and Future Plans

We provide an overview of the research plans for theCSCAPES Institute, funded by the Department of En-ergy’s SciDAC program for five years. Then we discussnew graph models and algorithms for the specialized graphcoloring problems that arise in computing Jacobians andHessians. Among these is the first practical algorithm foracyclic coloring and its use in estimating Hessians by anindirect method. We also evaluate the performance gainedthrough our coloring software in an automatic differentia-tion code.

Assefaw H. GebremedhinComputer Science DepartmentOld Dominion Universityassefaw@cs.odu.edu

Alex PothenOld Dominion UniversityDept of Computer Sciencepothen@cs.odu.edu

MS31

Uncertainty Analysis for Flows with TemperatureDependent Material Properties

In this talk, we discuss the use of sensitivity analysis (thecomputation of derivatives of fluid quantities with respectto model parameters) in performing uncertainty analysisfor fluids with temperature dependent material properties.Experimental measurements of the free convection of cornsyrup and nonlinear, temperature dependent models of vis-cosity and thermal conductivity are evaluated.

Eric TurgeonPratt and Whitney of Canadaturgeon@polymtl.ca

Dominique PelletierDepartement de Genie MechaniqueEcole Polytechnique de Montrealdominique.pelletier@polymtl.ca

Jeff BorggaardVirginia TechDepartment of Mathematicsjborggaard@vt.edu

MS31

Moment Closure for the Macro-Micro FENEModel of Complex Fluids

We present some systematic moment closure models for theFENE models of polymeric fluids, and we illustrate theirvarious extensions and demonstrate the good agreementwith the fully coupled macro-micro model for the simpleshear flow and extensional flows. The talk is based on thejoint works with YunKyong Hyon, Chun Liu and Peng Yu.

Qiang DuPenn State University

108 CS07 Abstracts

Department of Mathematicsqdu@math.psu.edu

MS31

A Two-Level Smagorinsky Model

A two-level method for discretizing the Smagorinsky modelfor the numerical simulation of turbulent flows is proposedand analyzed. The two-level algorithm consists of solvinga small nonlinear system of equations on the coarse mesh,and then using that solution to solve a larger linear systemon the fine mesh. For an appropriate choice of grids, thetwo-level algorithm is significantly more efficient than thestandard one-level algorithm.

Hyesuk LeeClemson UniversityDep. of Mathematical Scienceshklee@clemson.edu

Jeff Borggaard, Traian IliescuVirginia TechDepartment of Mathematicsjborggaard@vt.edu, iliescu@math.vt.edu

MS31

New Numerical Techniques for Some Non-Newtonian Flow Simulations

In this talk, we report efficient methods to simulate variousrate-type non-Newtonian fluid models in a unified frame-work. The method is developed from a simple observationthat various rate-type constitutive equations can be recastinto the well-known symmetric matrix Riccati differentialequations. We discuss and show how such an observationcan be crucially used for the stability with respect to thehigh Weissenberg number. The multigrid solution strategyfor the discrete system will also be presented and analyzed.

Young-Ju LeeMathematics DepartmentUCLAyjlee@math.ucla.edu

MS32

Moderator

John LowengrubDepartment of MathematicsUniversity of California at Irvinelowengrb@math.uci.edu

MS33

IMPETUS for Career Success

We present our Roller Coaster Camp outreach programdesigned for 7th-12th graders. We use an integrated math-physics curriculum to teach students about roller coasterdesign. The program helps build students basic skills whileintroducing them to exciting applications of computationalscience and engineering. We describe the hands-on learn-ing experiences, including a trip to Six Flags for rollercoaster research. We also incorporate professional devel-opment for teachers, undergraduate and graduate studentsto ultimately increase the awareness of STEM college pro-

grams and careers.

Peter R. TurnerClarkson UniversityMathematics and Computer Science Departmentpturner@clarkson.edu

David Wick, Michael Ramsdell, Kathleen FowlerClarkson Universitywickdp@clarkson.edu, ramsdemw@clarkson.edu,kfowler@clarkson.edu

MS33

The St. Lawrence Mathematics Partnership

This talk focuses on a partnership developed with NYState funding. The partnership is focused on professionaldevelopment activities for 300 teachers in a very widelyscattered, low income, rural part of northern New York.The primary objective is helping teachers appreciate theinteractions among science, mathematics and technologyfor solving real-world problems CSE at the K-12 level.Teachers work in triads throughout the year and attendweek-long institutes in the summer. Content examples andstructure will be presented.

Gail GothamSt Lawrence Lewis BOCESNYggotham@sllboces.org

Peter R. TurnerClarkson UniversityMathematics and Computer Science Departmentpturner@clarkson.edu

MS33

Title Not Available at Time of Publication

Abstract not available at time of publication.

Osman YasarState University of New YorkDepartment of Computational Sci.oyasar@brockport.edu

MS34

Formulation of a Target-Matrix Paradigm for MeshOptimization

A new target-matrix paradigm for improving mesh qual-ity by node repositioning via optimization is formulatedto place most application goals within a single theoreticalframework. The paradigm shifts the focus from qualitymetrics that measure quality in an absolute sense to met-rics that measure quality relative to application require-ments. In this talk, properties of mesh-based matrices, ofquality metrics and examples of objective functions will bepresented.

Patrick KnuppSandia National Laboratoriespknupp@sandia.gov

MS34

Implementation of the Target-Matrix Paradigm in

CS07 Abstracts 109

Mesquite

The design of the Mesquite quality improvement libraryhas been modified and extended to support a target-basedsmoothing paradigm. The design has been modified suchthat definition of the sample points at which a quality met-ric is evaluated in a patch of mesh has been abstracted.The design has been extended to allow target-based met-rics evaluated at user-specified element sample locations.

Jason KraftcheckThe University of Wisconsinkraftche@cae.wisc.edu

MS34

The Effect of Node Ordering on 2D Local MeshSmoothing

Local mesh smoothing is widely used for quality improve-ment of unstructured meshes due to its simplicity. One in-teresting aspect of this approach is the role of node orderingwithin a single pass over the mesh. We investigate variousordering schemes based on mesh quality, and the trade-offsinvolved between ordering and overall performance of theoptimization algorithm in terms of speed and quality im-provement. The study uses the FeasNewt solver within theMesquite package.

Suzanne M. ShontzDepartment of Computer Science and EngineeringThe Pennsylvania State Universityshontz@cse.psu.edu

Patrick M. KnuppSandia National Laboratoriespknupp@sandia.gov

MS34

Convexity of Mesh Optimization Metrics Using aTarget Matrix Paradigm

We discuss sufficient conditions for establishing convexityof mesh metrics within a target-matrix paradigm for meshoptimization that Patrick Knupp introduced at Sandia Na-tional Laboratories in 2006 in his SAND document SAND2006-2730J, titled A Target-Matrix Paradigm for Mesh Op-timization. We develop fairly simple criteria for provingconvexity of mesh metrics and certain objective functionsderived from those mesh metrics.

Evan VanderzeeUniversity of Illinoisvanderze@uiuc.edu

MS35

High Order Mimetic Differential Operators

Mimetic Operators satisfy a discrete analog of the diver-gence theorem and they are used to create or design con-servative andreliable numerical representations to contin-uous models. We will present a methodology to constructmimetic versions of the divergence and gradient operatorswhich exhibit high order of accuracy at the grid interioras well as at the boundaries. As a case of study, we willshow the construction of fourth order operators in a one-dimensional staggered grid. Mimetic conditions on discreteoperators are stated using matrix analysis and the overallhigh order of accuracy determines the bandwidth parame-ter. This contributes to a marked clarity with respect to

earlier approaches of construction. As test cases, we willsolve 2-D elliptic equations with full tensor coefficients aris-ing from oil reservoir models. Additionally, applications toelastic wave propagation under free surface and shear rup-ture boundary conditions will be given.

Jose CastilloSan Diego State UniversityComputational Science Researchcastillo@myth.sdsu.edu

MS35

Mimetic Discretizations for a Scalar Convection-Diffusion Operator

In this work, we presents two mimetic discretizations fora scalar convection-diffusion operator in 2D using Robinboundary conditions. Also, we have implemented otherdiscretization called support operator method. The nu-merical results show the performance about of the sparselinear solver and the convergence rate. We can observethat the mimetic methods has a good future

German A. LarrazabalUniversidad De CaraboboValencia-Venezuelaglarraza@uc.edu.ve

MS35

Mimetic Discretization of Elliptic Problems withFull Tensor Coefficients

This work concentrates on the Mimetic discretization ofelliptic partial differential equations (PDE), derived fromthe application of Darcys law to flows in Reservoir Simu-lation. Numerical solutions are obtained and discussed forone-dimensional equations on uniform and irregular gridsand two-dimensional equations on uniform grids. The focalpoint is to develop a scheme incorporated with the full ten-sor coefficients on uniform grids in 2-D. The results of thenumerical examples are then compared to previous well-established methods. Based on its conservative propertiesand global second order of accuracy, this Mimetic schemeshows higher precision in the tests given, especially on theboundaries.

Huy K. VuSpawar Systems CenterHuy Vu ¡huykhanhvu@yahoo.com¿

MS35

A Compatible Arbitrary Lagrangian-Eulerian Dis-cretization of the Magnetic Dynamo Equation

We are concerned with the simulation of coupledelectromagnetic-hydrodynamic-thermal systems, and wehave adopted an unstructured finite element ArbitraryLagrangian-Eulerian formulation for this problem. The fo-cus of this presentation is on the magnetic dynamo equa-tion, which is a vector advection-diffusion equation with animplied divergence-free constraint. We derive a variant ofconstrained transport with flux correction that is valid for3D unstructured grids, the algorithm relies heavily uponthe compatible (mimetic) curl operator.

Daniel WhiteLawrence Livermore National Laboratorywhite37@llnl.gov

110 CS07 Abstracts

MS36

Benchmarking Adaptive Multivariate SurrogateModeling Techniques

The increasing computational complexity of computer sim-ulation codes and the need for high fidelity simulationof large scale systems, has caused cheap meta-models tobecome standard practice in engineering design. Due totheir compact representation and efficient implementation,these surrogate models allow fast exploration of the de-sign space and extensive what-if analysis. In this con-tribution we compare three multivariate surrogate model-ing techniques: rational functions, multi-layer perceptronsand support vector machines. Both predefined functionsand real world engineering problems are used to checkthe performance of the meta-models. The results revealthe strengths and weaknesses of the different metamodeltypes and demonstrate the importance of adaptive meta-modeling and sequential design.

Dirk Gorissen, Wouter Hendrickx, Tom B. DhaeneUniversity of Antwerpdirk.gorissen@ua.ac.be, wouter.hendrickx@ua.ac.be,tom.dhaene@ua.ac.be

MS36

Structure-Preserving Model Reduction withoutUsing Explicit Projection

In recent years, there has been a lot of progress in Krylovsubspace-based structure-preserving model reduction oflarge-scale linear dynamical systems. However, all exist-ing methods first generate a basis matrix of the underlyingKrylov subspace and then employ explicit projection usingsome suitable partitioning of the basis matrix to obtain astructure-preserving reduced-order model. There are twomajor problems with the use of such explicit projections.First, it requires the storage of the basis matrix, whichbecomes prohibitive in the case of truly large-scale lineardynamical systems. Second, the approximation propertiesof the resulting structure-preserving reduced-order modelsare far from optimal, and they show that the available de-grees of freedom are not fully used. In this talk, we discussKrylov subspace-based recduction techniques that do notrequire explicit projection and thus overcome the two ma-jor problems of projection methods.

Roland W. FreundUniversity of California, DavisDepartment of Mathematicsfreund@math.ucdavis.edu

MS36

All Levels Reduced Order Models of Passive Inte-grated Components

Abstract not available at time of publication.

Wil SchildersNXP Semiconductors, Researchw.h.a.schilders@tue.nl

Daniel IoanPUB - LMN, Romaniadaniel@lmn.pub.ro

MS36

Linear and Nonlinear Model Order Reduction for

Nanoelectronics

Simulation for nanoelectronics requires that circuit equa-tions are coupled to electromagnetics, semiconductor equa-tions, and involves heat transfer. Model Order Reduction(MOR) is a means to speed up simulation. We discussapproaches to generalize existing MOR techniques to beapplicable to the resulting system of (Partial) Differential-Algebraic Equations. Also the inclusion of nonlinearity willbe taken into account. Experiences with several approacheswill be shown.

E. Jan W. ter MatenNXP Semiconductors, Research, DMS-PDMJan.ter.Maten@NXP.com

Arie VerhoevenEindhoven University of Technologya.verhoeven@tue.nl

Thomas VossDelft University of Technologyt.voss@tudelft.nl

Patricia AstridShell Global Solutions, Amsterdamp.astrid@shell.com

Tamara BechtoldNXP Semiconductors, Research, DMS-PDMtamara.bechtold@nxp.com

Evgenii RudnyiCADFEM GmbHGrafing b. Munchenevgenii@rudnyi.ru

MS37

Scalability and Run Time Support Issues

Traditional approaches to implementing scalable applica-tions are based on synchronous parallelism, which dividesan application into distinct phases of communication andcomputation. However, in some cases an asynchronousmodel is more appropriate. Such a model is better matchedto applications modeling asynchronous processes; it cansimplify the design of algorithms that tolerate communica-tion delays by overlapping them with computation. Thistalk will explore asynchronous programming techniquescurrently under investigation and discuss experiences withapplications.

Scott B. BadenDepartment of Computer Science and EngineeringUniversity of California, San Diegobaden@ucsd.edu

MS37

On a Future Software Platform for DemandingMulti-Scale and Multi-Physics Problems

Demanding problems in computational biology andmedicine span a range of scales and involve many differenttypes of mathematical models (for example, ODEs for cellbiology; PDEs for flow, tissue deformation, and eletricalsignals). Successful software must flexibly combine a vari-ety of models and numerical techniques in legacy and newcodes. In this talk we propose a Python-based platform

CS07 Abstracts 111

for future simulation software, where alternative legacy li-braries (such as PETSc, Trilinos, DOLFIN, Diffpack) canbe invoked in convenient ways and where new optimizedcode can be automatically generated. Examples on use-ful tools to realize such a platform will be given. We willalso demonstrate current progress with building completesolvers.

Ola SkavhaugSimula Research Laboratoryskavhaug@simula.no

Hans Petter LangtangenDepartment of Scientific ComputingSimula Research Laboratory and University of Oslohpl@simula.no

Xing CaiSimula Research Laboratory1325 Lysaker, Norwayxingca@simula.no

Kent-Andre MardalUniversity of OsloDepartment of Informatics,kent-and@simula.no

MS37

Multi-Scale Computational Modeling of the Heart

Computational models of the heart can be integrative inseveral important ways. In particular, multi-scale compu-tational models aim to achieve structural integration acrossphysical scales of biomedical organization from molecule toorganism. We describe and illustrate a strategy for devel-oping multi-scale models of the electromechanical proper-ties of the heart that integrate across the following scales:DAE network models of the biophysical mechanisms of cellexcitation and contractile processes and their biochemi-cal regulation. Structurally based constitutive models ofmulti-cellular tissue electrical and mechanical properties.PDE continuum models of cardiac wall mechanics and elec-trical impulse propagation in anatomically detailed modelsof the ventricles Closed loop systems models of pulmonaryand systemic circulatory dynamics.

Andrew D. McCullochDepartment of BioengineeringUniversity of California San Diegoamcculloch@ucsd.edu

Stuart CampbellUCSD Bioengineeringsgcampbe@ucsd.edu

Roy KerckhoffsUCSDDepartment of Bioengineeringroy@bioeng.ucsd.edu

MS37

Design Principles of Neurotransmitter Release dur-ing Synaptic Transmission: Calcium Imaging, Elec-trophysiology, and Spatially Realistic Monte CarloSimulations

Intracellular calcium is tightly regulated and is critical tomany processes, including nerve-evoked release of neuro-

transmitter molecules during synaptic transmission. Cal-cium imaging can be used to visualize spatiotemporalchanges that occur with nerve stimulation, and electro-physiological recordings can provide a readout of resultingneurotransmitter release. To understand the biophysicalcoupling between the two, we have created a 3-D model ofthe nerve active zone, the region from which neurotrans-mitter is released. The model is based on anatomical datafrom electron microscopy, was created with computer-aideddesign software, and subsequently was imported into theMCell/DReAMM environment for spatially realistic mi-crophysiological simulations (www.mcell.psc.edu). Usinga variety of experimental constraints and validations, wesimulate stimulus-driven calcium influx and binding withinan entire active zone using Monte Carlo diffusion-reactionalgorithms. We thus are able to predict important spatialand chemical kinetic relationships between voltage-gatedcalcium channels, synaptic vesicles, calcium binding sites,and neurotransmitter release. Model predictions then canbe tested using experimental (pharmacological) perturba-tions that change the incoming calcium signal in differentways. This combination of experiment and spatially real-istic Monte Carlo modeling yields insights that cannot beobtained in other ways, and that illustrate physiologicallyimportant design principles for high sensitivity, fidelity,and adaptability of neurotransmitter release. Supportedby NIH R01 GM068630 and P41 RR06009.

Joel R. StilesPittsburgh Supercomputing CenterCarnegie Mellon Universitystiles@psc.edu

MS38

A Multilevel Optimization Approach to PDE-Constrained Optimization

We examine an approach to the design of complex systemsgoverned by coupled PDE. The term multilevel refers tothe optimization problem formulation, the solution algo-rithm and the use of several layers of models in represent-ing a particular discipline at various stages of design. Weinvestigate analytical and computational properties of theapproach and examine a numerical demonstration.

Natalia AlexandrovNASA Langley Research Centern.alexandrov@nasa.gov

MS38

Optimal Control of Elliptic Variational Inequalities

The class of control problems considered in this talk fallsinto the area of mathematical programs with complemen-tarity constraints (MPCCs) in function space. Theseproblems typically violate classical constraint qualifications(such as the Mangasarian-Fromovitz constraint qualifica-tion) and, hence, the existence of (Lagrange) multipliersdoes not follow from standard theory. In this talk, basedon a relaxation scheme for the complementarity constraintwe derive first order optimality characterizations, which,after passing to the limit, provide first order conditions forthe MPCC. Then an algorithmic framework is presentedwhich is based on a Moreau- Yosida-based path-followingconcept in order to deal with poor multiplier regularity.The talk ends by a report on numerical results.

Michael HintermuellerUniversity of Graz

112 CS07 Abstracts

Austriamichael.hintermueller@uni-graz.at

MS38

Solution of Optimal Control Problems Arising inthe Modeling and Design of Semiconductors

Optimization problems governed by the drift–diffusionequations that arise in the modeling of semiconductor de-vices present many algorithmic and analytic challenges.The first part of the talk focuses on algorithmic issuesin solving a real–world large–scale semiconductor designproblem, in particular the use of a novel trust–region SQPalgorithm that allows inexact (e.g. iterative) linear systemsolves. The second part addresses analytic issues relatedto the fact that the objective functionals of interest involveflux terms, which have fundamentally different discrete rep-resentations depending on which FE scheme is used for thediscretization of the underlying PDEs.

Denis RidzalSandia National Laboratoriesdridzal@sandia.gov

MS38

Approximate Reduced SQP Approaches for Aero-dynamic Shape Optimization

Aerodynamic shape optimization is still a challenging sub-ject. Recently, novel highly efficient algorithms based onapproximate reduced SQP methods have been developed.Numerical results for practical problems provided by DLRGermany within the joint effort MEGADESIGN are pre-sented as well as theoretical insights.

Volker H. SchulzDepartment of Mathematics, University of Trierschulzv@uni-trier.de

MS39

3D Multi-Material Interface Reconstruction withGeneral Polyhedral Meshes

We present a 3D volume tracking multi-material in-terface reconstruction algorithm for general polyhedralmeshes. Multiple piecewise linear interfaces are recon-structed within polyhedral cells containing more than twomaterials. Second order accurate interface reconstructionalgorithms, such as LVIRA and MoF, are applied for gen-eral polyhedral mesh environment. Multi-material order-ing algorithms are presented for proper sequence of inter-face reconstruction. For maximum flexibility of handlingcomplex geometries as well as arbitrary mesh motion, gen-eral polyhedral meshes are utilized.

Mikhail Shashkov, Hyung T. AhnLos Alamos National Laboratoryshashkov@lanl.gov, htahn@lanl.gov

MS39

Mimetic Discretization Methods

Compatible discretizations are model reduction techniquesto replace PDE’s by algebraic equations that mimic theirfundamental structural properties. We provide a commonframework for such discretizations using algebraic topologyto guide our analysis. This results in discrete notions of dif-ferentiation and integration that are mutually consistent in

the sense that they obey a discrete Stokes theorem. Fur-thermore, the invariants of DeRham homology groups arepreserved in a discrete sense, which allows, among otherthings, for an elementary calculation of the kernel of thediscrete Laplacian. The key components of the frameworkare a restriction operator defined by the DeRham mapand a consistent reconstruction operator. We show thatmany of the existing compatible discretizations by finiteelements, finite volumes and finite differences are obtainedfrom the framework by specific choices of the reconstruc-tion operator. This opens up an attractive possibility todevelop a common convergence and stability analysis for abroad range of discrete models.

Pavel BochevSandia National LaboratoriesComputational Math and Algorithmspbboche@sandia.gov

MS39

Stabilized Lagrangian Hydrodynamics

A new SUPG-stabilized formulation for Lagrangian Hy-drodynamics of materials satisfying the Mie-Gruneisenclass of constitutive laws is presented [(Guglielmo Scov-azzi, Mark A. Christon, Thomas J. R. Hughes, and JohnN. Shadid, ”Stabilized shock hydrodynamics: I. A La-grangian method”, (accepted, Computer Methods in Ap-plied Mechanics and Engineering, 2006),Guglielmo Sco-vazzi, ”Stabilized shock hydrodynamics: II. Design andphysical interpretation of the SUPG operator for La-grangian computations”, (accepted, Computer Methods inApplied Mechanics and Engineering, 2006).]. The proposedmethod can be used in conjunction with simplex-type (tri-angular/tetrahedral) meshes, as well as the more com-monly used brick-type (quadrilateral/hexahedral) meshes.Simplex-type meshes offer significant advantages in the au-tomatic mesh generation process, and they are usually pre-ferred in multi-physics problems involving radiation effects.The proposed method results in a globally conservativeformulation, in which equal-order interpolation (P1 or Q1isoparametric finite elements) is applied to velocities, dis-placements, and thermodynamic variables, namely pres-sure. As a direct consequence, a natural representationof the pressure gradient on element interiors bypasses allproblematic issues related to pressure gradient reconstruc-tion, typical of standard, cell-centered, multidimensionalhydrocode implementations. SUPG stabilization in theLagrangian context involves specific design requirementssuch as Galilean invariance [Guglielmo Scovazzi, ”A dis-course on Galilean invariance, SUPG stabilization, and thevariational multiscale framework”, (accepted, ComputerMethods in Applied Mechanics and Engineering, 2006).],an overlooked aspect in the literature on the subject. Adiscontinuity capturing operator in the form of a Noh-typeviscosity with artificial heat flux is used to preserve sta-bility and smoothness of the solution in the shock regions.Numerical results for the Euler equations of gas dynamicswill be presented.

Mark ChristonLos Alamos National Laboratorieschriston@lanl.gov

John ShadidSandia National LaboratoriesAlbuquerque, NMjnshadi@sandia.gov

Guglielmo Scovazzi

CS07 Abstracts 113

Sandia National Laboratoriesgscovaz@sandia.gov

Thomas J. R. HughesICES, The University of Texas at Austinhughes@ices.utexas.edu

MS39

Closure Models for Mixed Cells in Multi-MaterialFlow Simulations

High-speed multi-material flows with strong shear defor-mations occur in many problems. Due to the nature ofshock wave propagation in complex materials, the Arbi-trary Lagrangian-Eulerian (ALE) methods are currentlythe only proven technology to solve such problems. In ALEmethods, the mesh does not move with the fluid, and soit is unavoidable that mixed cells containing two or morematerials will appear, and special closure model is neededfor such cells.

Misha ShashkovLos Alamos National LaboratoryGroup T-7, MS B284shashkov@lanl.gov

MS40

Computational Studies of Nematic Liquid Crys-talline Polymers in Planar Shear Flow

Abstract not available at time of publication.

Carlos J. Garcia-CerverUCSBcgarcia@math.ucsb.edu

MS40

Numerical Results on Flow-Driven Responses forAnisotropic Nematic Liquid Crystals and ParticleSuspensions

Abstract not available at time of publication.

Qi WangFlorida State UniversityDepartment of Mathematicswang@math.fsu.edu

MS40

Comprehensive Study of 2D Nematic Polymers Un-der a Shear

We study the behavior of 2D nematic polymers under sshear of arbitrary magnitude. When the shear is weak,the previous asymptotic analysis showed that there existsa threshold (U0) for the normalized polymer concentration(U) such that for U¡U0 the polymer orientation distribu-tion converges to a steady state; for U¿U0 the polymerorientation distribution tumbles and does not converge toa steady state. Numerical results show that as the magni-tude of the shear increases the magnitude of the thresholdalso increases. We will discuss the change of U0 and thechange in behaviors of the polymer orientation distributionas the magnitude of the shear increases.

Hongyun WangUniversity of California, Santa Cruzhongwang@soe.ucsc.edu

MS40

Anchoring-Induced Texture and Shear Banding ofNematic Polymers in Shear Cells

We numericall explore texture and shear banding of ne-matic polymers in shear cells, allowing for one-dimensionalmorphology in the gap between parallel plates. We solvethe coupled Navier-Stokes and Doi-Marrucci-Greco orien-tation tensor model, considering both confined orientationin the plane of shear and full orientation tensor degrees offreedom. This formulation makes contact with a large lit-erature on analytical and numerical as well as experimentalstudies of nematic polymer texture and flow feedback.

Qi WangFlorida State UniversityTallahassee, FL 32306wang@mail.math.fsu.edu

M. Gregory ForestUniversity of North CarolinaChapel Hill, NC 27599forest@amath.unc.edu

Hong ZhouDepartment of Applied MathematicsNaval Postgraduate School, Monterey, CAhzhou@nps.edu

MS41

A One-Dimensional Conservative Method to TrackDiscontinuities in a Compressible Medium

We present a multi-fluid method where a moving interfacecuts out time-varying control volumes. A consistent finite-volume discretization is derived by applying the divergencetheorem in space and time, and the resulting method isfully conservative even at the discontinuities. The trunca-tion errors are expected to be first-order at the interface,which is one order higher than conventional methods. Bothshock waves and contact discontinuities are presented aspossible interfaces in the results. UCRL-ABS-223489.

Caroline Gatti-Bono, David TrebotichLawrence Livermore National Laboratorycbono@llnl.gov, trebotich1@llnl.gov

Phillip ColellaLawrence Berkeley National LaboratoryPColella@lbl.gov

MS41

A Second-Order Accurate Level Set Method onNon-Graded Adaptive Cartesian Grids

We will present a level set method on non-graded adaptiveCartesian grids, i.e. grids for which the ratio between ad-jacent cells is not constrained. We use quadtree and octreedata structures to represent the grid and a simple algo-rithm to generate meshes with the finest resolution at theinterface. In particular, we will present (1) a locally thirdorder accurate reinitialization scheme that transforms anarbitrary level set function into a signed distance function,(2) a second order accurate semi-Lagrangian methods toevolve the linear level set advection equation under an ex-ternally generated velocity field, (3) a second order accu-rate upwind method to evolve the nonlinear level set equa-tion under a normal velocity as well as to extrapolate scalarquantities across an interface in the normal direction, and

114 CS07 Abstracts

(4) a semi-implicit scheme to evolve the interface undermean curvature. Combined, we obtain a level set methodon adaptive Cartesian grids with a negligible mass loss. Wewill exemplify the performance of the method in two andthree spatial dimensions.

Frederic GibouUC Santa Barbarafgibou@engineering.ucsb.edu

Chohong MinDepartment of MathematicsUniversity of Californiachohong@math.ucsb.edu

MS41

A Volume-of-Fluid Method for Compressible Mul-tiphase (Resolved) Flow

A finite volume method will be presented for the model-ing of compressible flows consisting of multiple spatially-resolved material phases. The approach uses well-knownhigh-order Godunov methods to advance individual mate-rial regions. Interfaces are reconstructed from volume-of-fluid fields advected with velocities obtained from interfa-cial 2-material Riemann problems. Cut cell conservationand stability is maintained with the mass-redistributionformalism. This approach is stable and globally O(h) forcharacteristic variables. Example solid-solid-vacuum calcu-lations in 3d will be presented. The convergence propertieswill motivate higher-order methods being developed by C.Bono and P. Colella.

Gregory H. MillerUC Davis & LBNLgrgmiller@ucdavis.edu

Phillip ColellaLawrence Berkeley National LaboratoryPColella@lbl.gov

MS41

A N-Dimensional Conservative Front-TrackingMethod

We present a N-dimensional conservative interface trackingalgorithm with a convex hull control volume reconstructionmethod based on a grid-based space-time interface. Thealgorithm is derived from an integral formulation of PDEs.Near tracked discontinuities in the solution, the proposedalgorithm improves by one order in its errors commonlyfound near a discontinuity.

Zhiliang XuUniversity of Notre Damezxu2@nd.edu

Jingjie LiuSUNY at Stony Brookjingjie@ams.sunysb.edu

James G. GlimmSUNY at Stony BrookDept of Applied Mathematicsglimm@ams.sunysb.edu

Xiaolin LiDepartment of Applied Math and Stat

SUNY at Stony Brooklinli@ams.sunysb.edu

MS42

Verification Analysis of NNSA Tri-Lab Test SuiteProblems

Three DOE laboratories identified test problems used toevaluate hydrocode performance. We describe error mod-els used in these assessments and propose how they couldbe expanded. Automated analysis of two- and three-dimensional problems provide results on how well hy-drocodes retain fidelity to the underlying physics when mo-tions and gradients are not grid-aligned. We include anassessment of whether solutions using an adaptive meshrefinement algorithm are as accurate as solutions on corre-sponding uniform grids.

James Kamm, Frank Timmes, Francois HemezLos Alamos National Laboratorykammj@lanl.gov, timmes@lanl.gov, hemez@lanl.gov

MS42

Code Verification for Astrophysical SimulationCodes

Verification of astrophysical simulation codes poses uniquechallenges. Codes may have to solve equations that de-scribe the dynamics of matter, radiation, magnetic fields,and the gravitational field. It is important that each ofthese components be verified using standard techniquesappropriate for specific sets of equations, e.g. the Eulerequations. Verification of the coupled sets of equations isequally important. We will discuss verification of astro-physical simulation codes and areas where more work isneeded.

Doug SwestySUNY at Stony BrookDept. of Physics & Astronomydswesty@mail.astro.sunysb.edu

MS42

Qualitative and Quantitative Accuracy of the Lat-tice Boltzmann Method

Many methods have been developed to study hydrody-namics. While very accurate, some approaches requirelaborious set-up and suffer from computational complex-ities, such as, frequent re-meshing. The lattice Boltzmannmethod, a discretized form of the Boltzmann TransportEquation, has shown promise for solving complex fluidproblems. A brief overview of the method is presentedand results are compared with theory and other estab-lished computational methods. Examples include porousmedia and particulate flows, natural convection, and mi-crofluidics.

Todd Weisgraber, David ClagueLawrence Livermore Nat’l Labweisgraber2@llnl.gov, clague1@llnl.gov

MS42

Verification of Multiphysics Codes

We will present results of a formal a verification effort ofa multi-physics code through use of observed spatial andtemporal order-of-accuracy. Formal verification requires

CS07 Abstracts 115

development of appropriate test cases targeting importantcodes modules, construction and review of input decks forthe code, and grid refinement studies. We will discuss de-cision points in the formal verification and outline advan-tages and disadvantages of each choice. This work wasperformed under the auspices of the U. S. Department ofEnergy by University of California Lawrence Livermore Na-tional Laboratory under Contract W-7405-Eng-48.

Carol S. WoodwardLawrence Livermore Nat’l Labcswoodward@llnl.gov

Kambiz SalariLawrence Livermore Nat’l LabCASCsalari@llnl.gov

Steve AndersonLawrence Livermore Nat’l Labanderson28@llnl.gov

MS43

New Approaches to Optical Flow and Digital In-painting

In this talk, new formulation for the optical flow problemand digital inpainting problem are presented. For deter-mining optical flows, an optimal control approach is pre-sented where the velocity field are interpreted as bilinearcontrol functions of the optimal control problem of trackinga sequence of given frames. This approach was originallyproposed in A. Borz, K. Ito, and K. Kunisch, SIAM J. Sci.Comput., 24(3) (2002), 818-847. For digital inpainting, anew approach based on the solution of a Ginzburg–Landauequation is discussed. This approach was first proposedin H. Grossauer and O. Scherzer, Scale Space Methodsin Computer Vision, Lecture Notes in Computer Science2695, Springer, 2003.

Alfio BorziUniversity of GrazInstitute for Mathematics and Scientific Computingalfio.borzi@uni-graz.at

MS43

Super Fast OcTree Representations

Abstract not available at time of publication.

Eldad HaberEmory UniversityDept of Math and CShaber@mathcs.emory.edu

MS43

Registration and Intensity Correction

In many medical applications, registration and intensitycorrection problems do intertwine. We propose a newmethodological framework for a joint registration and in-tensity correction (RIC). This framework is based on min-imization of a joint energy J with various degrees of free-dom. The essential advantages of the RIC approach are:combination of registration and intensity correction intoone unified framework and thus joint minimization. Theperformance of the RIC approach is demonstrated on a

variety of applications ranging from MRI to histology.

Jan ModersitzkiUniversity of Luebeck, GermanyInstitute of Mathematicsmodersit@math.mu-luebeck.de

MS43

Volume Preserving Image Registration

There exist many instances particularly in medical imagingwhich demand for registration. Many applications requirethat the transformation that deforms the template imagehas to be one-to-one. We force bijectivity by controllingthe change of volume of the transformation and presentvariational techniques to prove the existence of a minimiz-ing element of this constrained optimization problem. Fur-thermore we propose conditions on registration functionalsthat guarantee the existence of minimizing elements.

Christiane PoschlUniversity of InnsbruckInstitute of Computer Sciencemailto:Christiane.Poeschl@uibk.ac.at

Jan ModersitzkiLuebeck Universitymodersitzki@math.uni-luebeck.de

Otmar ScherzerUniversity Innsbruckotmar.scherzer@uibk.ac.at

MS44

Computing Viscoelastic Fluid Flows at High Weis-senberg Number

The numerical simulation of viscoelastic fluid flow becomesmore difficult as a physical parameter, the Weissenbergnumber, increases. Specifically, for a given discretizationscheme and set of problem parameters, standard nonlinearsolution approaches fail to converge beyond a critical valueof the Weissenberg number. In this talk we discuss thesteady-state Johnson-Segalman model for viscoelastic fluidflow and the high Weissenberg number problem. We ex-amine the behavior of computed solutions near the criticalWeissenberg value, and investigate approaches to comput-ing solutions at and above the critical Weissenberg number.

Hyesuk LeeClemson UniversityDep. of Mathematical Scienceshklee@clemson.edu

Vincent J. Ervin, Jason HowellClemson Universityvjervin@clemson.edu, howell4@clemson.edu

MS44

Numerical Approximation of a Non-Linear Gener-alized Newtonian Fluid with Defective BoundaryConditions

We study the numerical approximation of a non-linear gen-eralized Newtonian fluid where only the flow rates are spec-ified for the inflow and outflow boundaries. A variationalformulation of the problem is developed based on the La-grange multipliers rule in order to enforce the stated flow

116 CS07 Abstracts

rates. Existence and uniqueness of the solution to thecontinuous, and discrete, variational formulation will beshown. An error estimate for the numerical approximationand some numerical results will be discussed.

Hyesuk LeeClemson UniversityDep. of Mathematical Scienceshklee@clemson.edu

Vincent J. ErvinClemson Universityvjervin@clemson.edu

MS44

Advances in MHD Flow Simulation

Magnetohydrodynamics (MHD) is the theory of the macro-scopic interaction of electrically conducting fluids with amagnetic field. It is of importance in connection with manyengineering problems such as plasma confinement, liquid-metal cooling of nuclear reactors, the CZ crystal growthprocess, and electromagnetic casting. In the viscous in-compressible case, MHD flow is governed by the Navier-Stokes equations and the pre-Maxwell equations giving riseto challenging problems of mathematical analysis and nu-merical approximation. We will discuss recent advances inMHD flow simulation.

Amnon J. MeirDepartment of Mathematics and StatisticsAuburn Universityajm@auburn.edu

Kang Jin, Paul SchmidtDepartment of Mathematics and StatisticsAuburn Universityjinkang@auburn.edu, pgs@auburn.edu

MS44

Index Reduction Approaches for Feedback Controlof the Navier-Stokes Equations

Linear feedback control is considered for large systems ofdifferential algebraic equations arising from discretizationof saddle point problems. Necessary conditions are derivedby applying the Maximum Principle and have the form ofconstrained Riccati equations. We consider two approachesfor solving the feedback control problem as well as practi-cal numerical methods. Numerical studies using examplesderived from a constrained heat equation and the Stokesequation demonstrate the effectiveness of the approacheswe consider.

Miroslav StoyanovDepartment of MathematicsVirginia Techstoyanov@math.vt.edu

MS45

Moderator

Christopher JohnsonUniversity of UtahDepartment of Computer Sciencecrj@sci.utah.edu

MS46

Patterns on Growing Square Domains Via ModeInteraction

We consider reaction-diffusion systems on growing squaredomains with Neumann boundary conditions (NBC). Assuggested by numerical simulations, we study the simplerproblem of mode interactions in steady-state bifurcationproblems with both translational symmetry and squaresymmetry, combined with the symmetry constraint im-posed by NBC. We show that the transition between differ-ent types of squares can be generically continuous. Also, weshow that transitions between squares and stripes can oc-cur generically via a jump, via steady-states or via steady-states and time-periodic states. We point out some differ-ences between stable patterns in the NBC problem and inthe periodic boundary conditions problem. This is jointwork with Martin Golubitsky.

Adela ComaniciRice Universityadelanc@math.vt.edu

MS46

Modelling the Origin of Pattern in Naevoid SkinDisease: A Survey of Recent Results

A diffusing system of interacting chemical species restrictedto the ectodermal surface of the primitive embryo is shown,via a two-species reaction-diffusion mdoel, to be capableof generating spatial inhomogeneity of chemical concen-tration. Depending on local concentrations, these chemi-cal ”pre-patterns” can then act as centres of organisationvia genetic switching, chemotaxis or differential rates ofgrowth. It is suggested the process may account for the ori-gin of the patchiness of naevoid skin disease. Many types ofmorphologies - from simple unilateral asymmetries to lines-of-Blaschko-like - can be generated by this simple and uni-versal scheme. Here some recent results are reported andthe implications for the pathogenesis of mosaic skin diseaseis discussed.

Stephen Gilmore

Senior Lecturer, Department of Medicine (Dermatology),St Vincent’s Hospital, Victoria, Australiasjgilmore@bigpond.com

MS46

Title Not Available at Time of Publication

Abstract not available at time of publication.

John LowengrubDepartment of MathematicsUniversity of California at Irvinelowengrb@math.uci.edu

MS46

Numerical Solutions of Reaction-Diffusion Systemson Continuously Growing Domains

We examine the implications of mesh structure on numeri-cally computed solutions of a reaction-diffusion model sys-tem on two-dimensional growing domains. The incorpora-tion of domain growth creates an additional parameter –the grid-point velocity – which greatly influences the se-lection of certain symmetric solutions for the ADI finitedifference scheme. Domain growth coupled with grid-point

CS07 Abstracts 117

velocity stabilises certain patterns which are unstable toany kind of mesh perturbation.

Anotida MadzvamuseUniversity of SussexDept of Mathematicsa.madzvamuse@sussex.ac.uk

MS47

Simulation of Magneto-Hydrodynamic PhysicsAssociated with Evolving Interfaces Via ALE-GRA/MESQUITE

Simulation of physics associated with severe deformationsand evolving interfaces may be treated with Arbitrary La-grangian Eulerian (ALE) techniques. The use of a La-grangian interface and evolving ALE regions introduces anumber of challenges for ALE mesh smoothing. We ex-plore the application of the MESQUITE library to addresssome of these issues. Specifically, we discuss several impor-tant ALEGRA-HEDP simulations where MESQUITE wasemployed to improve the usability of ALEGRA relative tomore traditional approaches. *Sandia is a multi-programlaboratory operated by Sandia Corporation, a LockheedMartin Company, for the United States Department ofEnergys National Nuclear Security Administration undercontract DE-AC04-94AL85000.

Thomas Voth, Christopher Garasi, Michael BrewerSandia National Laboratorytevoth@sandia.gov, cjgaras@sandia.gov,mbrewer@sandia.gov

MS47

Using Mesquite in Distributed Memory Applica-tions

We discuss the development of an infrastructure that sup-ports the use of Mesquite mesh quality improvement algo-rithms in distributed memory applications. We start withthe application’s decomposition of the mesh data and usean iterative process to select independent sets of verticesto resposition in each pass. We experiment with a mix oflocal and global techniques from Mesquite and report onthe scalability and performance or our methods.

Lori A. DiachinLawrence Livermore National Laboratorydiachin2@llnl.gov

Craig KapferLawrence Livermore National Labckapfer@llnl.gov

MS47

R-Adaptivity Using Finite Element Theoretical Er-ror Bounds

Mesh quality is critical for accuracy in the numerical so-lution of partial differential equations. In this talk, wewill review briefly theoretical bounds for the finite elementanalysis. We will emphasize the role of mesh quality inthese theoretical bounds. Then we will discuss how thesetheoretical results can influence the design of mesh opti-mization algorithms by vertex repositioning. Numericalexamples will illustrate the performance of this approach.

Ulrich L. HetmaniukSandia National Laboratories

ulhetma@sandia.gov

MS47

Improvement of Remapped Meshes UsingMesquite in ALE Applications

Adaptive Lagrangian Eulerian (ALE) techniques are com-monly used in numerical simulations of multidimensionalfluid flow. ALE methods typically use relatively simplegeometric approaches to combat deteriorating mesh qual-ity as the number of remaps increase. In these schemes,there are often no barriers to mesh element inversions andsolution behaviors are neglected which may lead to in-accuracies. To help address these issues, we apply theoptimization-based approaches in the Mesquite mesh qual-ity improvement software library to a particular ALE hy-drodynamics code. We show that this approach preserveslarge-scale features of the remapping, honors fixed internaland boundary nodes, and prevents element inversion.

Lori A. DiachinLawrence Livermore National Laboratorydiachin2@llnl.gov

Craig KapferLawrence Livermore National Labckapfer@llnl.gov

MS48

Hierarchical Model Reduction of Structured Ma-trices

The talk concentrates on the treatment of (large) struc-tured matrices in general, and in particular on matricesthat have multiple hierarchical structure of the semi sep-arable type. Such matrices occur e.g. in bulk or surfacefinite-element like systems, encountered in solving partialdifferential equations in the direct form or as integrals witha Green’s function. In the 1D case the resulting structureis invariably close to semi-separable matrix, and there ex-ists a well developed theory of model reduction for thiscase (which will be reviewed). In higher dimensions, thesituation is much more complicated, but not hopeless. Theproblem gets its richest expression when one considers effi-cient methods for matrix inversion, in which the hierarchi-cal structure of the original matrix is exploited to obtainefficiency. We give a survey of techniques that can be usedto handle this case, develop some theory on the model re-duction properties that can be obtained and illustrate themethods by example.

Patrick DeWildeDelft Univ of TechnologyFaculty EWIdewilde@cobalt.et.tudelft.nl

MS48

PPV-HB: Harmonic Balance for Oscillator/PLLPhase Macromodels

Oscillators feature unboundedly increasing phase charac-teristics when perturbed by external signals, making stan-dard harmonic balance (HB) inapplicable to their phasemacromodels. In this talk, we rectify this situation bypresenting a novel extension of HB that is capable ofhandling oscillator phase macromodels. Key to the newmethod, termed PPV-HB, is a formulation that separatesunboundedly increasing terms of phase characteristics from

118 CS07 Abstracts

bounded, periodic components. PPV-HB can be used notonly on individual oscillators, but crucially, it enables theapplication of HB-like techniques for simulating system-level equation systems composed of higher-level macromod-els of blocks. We validate PPV-HB on individual oscillatorsand a PLL system, demonstrating perfect matches withtransient simulation using phase macromodels. Speedupsof 1-2 orders of magnitude are obtained, in addition tospeedups of another 2-3 orders of magnitude that stemfrom using macromodels as opposed to full circuit simu-lation.

Ting MeiUniversity of MinnesotaECE Departmentmeiting@ece.umn.edu

MS48

Model-Compiler Driven Model Order Reductionand VLSI Circuit Simulation

Abstract not available at time of publication.

Richard ShiUniversity of Washington, Seattlecjshi@u.washington.edu

MS48

Direct Methods for Model Order Reduction of RCCircuits

In this presentation we will introduce direct techniques,as opposed to iterative (projection based) techniques, forsimplification of very large RC circuits arising during theelectrical modeling of integrated circuits. The principal ad-vantage of such techniques is to stay closer to the electricaldomain, rather than loosing essential properties related tothe physics of the problem as a result of the mathematicalprocess. As a result, the so-called realization problem isavoided or alleviated.

Nick van der MeijsDelft University of Technologynick@cobalt.et.tudelft.nl

MS49

Iterative Methods for Nonconvex PDE Con-strained Optimization

Interior methods are proposed for the numerical solution ofgeneral nonlinear PDE-constrained optimization problems.The talk will focus on methods based on sequential uncon-strained optimization and the use of multilevel precondi-tioned iterative methods for the constituent linear systems.Based on joint work with Randolph Bank, Anders Forsgrenand Joshua Griffin.

Philip E. GillUniversity of California, San DiegoDepartment of Mathematicspgill@ucsd.edu

MS49

Parallel Solution of Large-Scale Nonlinear Param-eter Estimation Problems with IPOPT

We present the next generation version of IPOPT with ca-pabilities for efficient parallel solution of large, structured

nonlinear programming problems. This nonlinear interiorpoint framework allows straightforward customization ofthe linear algebra data structures and calculation routines.A parallel Schur-complement decomposition has been im-plemented and scaleup results are demonstrated on a realdynamic parameter estimation problem.

Carl LairdChemical EngineeringCarnegie Mellon Universityclaird@andrew.cmu.edu

Victor Zavala, Lorenz BieglerChemical EngineeringCarnegie Mellon Universityvzavala@andrew.cmu.edu, lb01@andrew.cmu.edu

MS49

Inexact Primal-Dual Methods for Constrained Op-timization

Very large constrained optimization problems, such asthose arising in PDE-constrained optimization, can besolved using inexact methods in which the search direc-tion is computed using iterative linear algebra techniques.To make such an approach robust for nonlinear problems,it is necessary to know when an approximate solution ofthe primal-dual system makes sufficient progress towardoptimality. In this talk we consider conditions that en-sure global convergence using models of an exact penaltyfunction.

Richard H. ByrdUniversity of Coloradorichard@cs.colorado.edu

Frank E. CurtisNorthwestern Universityfecurt@gmail.com

Jorge NocedalDepartment of Electrical and Computer EngineeringNorthwestern Universitynocedal@eecs.northwestern.edu

MS49

Primal Dual Interior Point Methods for PDE Con-strained Optimization

Primal-dual interior-point methods have proven to be veryefficient in the context of large scale nonlinear program-ming. In this talk, we present a convergence analysis of aprimal-dual interior-point method for PDE-constrained op-timization in an appropriate function space setting. Con-sidered are optimal control problems with control con-straints in Lp. It is shown that the developed primal-dualinterior-point method converges globally and locally super-linearly. Not only the L∞-setting is analyzed, but also amore involved Lq-analysis, q < ∞, is presented. In L∞,the set of feasible controls contains interior points and theFrechet differentiability of the perturbed optimality sys-tem can be shown. In the Lq-setting, which is highly rel-evant for PDE-constrained optimization, these nice prop-erties are no longer available. Nevertheless, using refinedtechniques, a convergence analysis can be carried out. Inparticular, two-norm techniques and a smoothing step arerequired. Numerical results are presented.

Michael Ulbrich

CS07 Abstracts 119

Technical University of MunichChair of Mathematical Optimizationmulbrich@ma.tum.de

Stefan UlbrichTechnische Universitaet DarmstadtFachbereich Mathematikulbrich@mathematik.tu-darmstadt.de

MS50

A Novel In Silico Approach For De Novo ProteinDesign

The primary objective in de novo protein design is to deter-mine the amino acid sequences which are compatible withspecific template backbone structures that may be rigidor flexible. It is of fundamental importance since it ad-dresses the mapping of the space of amino acid sequences toknown protein folds or postulated/putative protein folds.It is also of significant practical importance since it canlead to the improved design of inhibitors, design of novelsequences with better stability, design of catalytic sites ofenzymes, and drug discovery. The de novo protein designproblem involves three key decisions: (a) the definition ofthe template backbone structure; (b) the sequence selec-tion; and (c) the validation of the fold specificity and foldstability. The template backbone structure can be (i) asingle rigid backbone (e.g., the average NMR structure fora protein); (ii) a set of rigid backbone structures (e.g., allNMR structures for a protein or a discrete number of ran-domly selected rigid structures based on some algorithmicprocedure or a discrete set of rigid structures based on aparameterization of the backbone); or (iii) a flexible back-bone structure defined by lower and upper bounds on thedistances between the alpha carbon atoms and the back-bone dihedral angles. It is apparent that true backbonetemplate flexibility is reflected in (iii) since it allows forall possible combinations of distances and backbone dihe-dral angles within their specified ranges, while (ii) consid-ers only a small subset of flexible structures, and (i) isrestricted to a single structure only. In this presentation,we will discuss a novel two stage approach which takes intoaccount explicitly the flexibility of the templates. The firststage addresses the in silico sequence selection problem viaa novel mathematical modeling and optimization approachwhich corresponds to the class of quadratic assignment-likemodels. It will be shown that these models can be solvedto global optimality rigorously. The second stage addressesthe fold specificity by performing structure prediction cal-culations using atomistic level force fields and the firstprinciples approach, Astro-Fold. The probabilities of eachsequence to fold specifically to the flexible templates arecalculated. The theoretical prediction results for severalsystems that include variants of Compstatin, human betadefensins, C3a, and gp41 of HIV-1 virus will be presented.

Chris FloudasDepartment of Chemical EngineeringPrinceton Universityfloudas@titan.princeton.edu

MS50

Optimization with Categorical or Integer Variables

Many optimal design applications are modeled using cat-egorical variables, that are not integers, and express forexample material choices. Such models do not allow stan-dard optimization techniques to be used, leading scientiststo use heuristic search procedures. We show, that categor-

ical variables can be modeled using standard 0-1 variables.We illustrate our approach on a thermal insulation system,which has a number of insulators of different materials (thecategorical variables) to minimize the heat flow.

Sven LeyfferArgonne National Laboratoryleyffer@mcs.anl.gov

Kumar AbhishekLehigh Universityabhishek@mcs.anl.gov

MS50

Optimizing Sensor Placement for Municipal WaterNetwork Security

We wish to optimally place sensors in water networks tominimize expected damage due to intentional or acciden-tal contamination. We track the movement of contamina-tion through a network using a simulator. In its simplestform, placing sensors to detect a suite of events is a p-median problem. We describe integer programming mod-els and heuristics for effectively solving full-scale problems.We discuss modifications to address uncertainties in im-pact values, contamination event distribution, objective,and sensor performance.

Cynthia PhillipsSandia National Laboratoriescaphill@sandia.gov

MS50

Vulnerability Analysis on The Electric Power Grid

We present our work on detecting the vulnerabilities ofthe electric power system, i.e., a small group of lines thatcan cause a significant blackout, if they fail concurrently.We model the problem as a mixed integer nonlinear opti-mization problem, and our analysis on the structure of anoptimal solution reveals a reduction to a pure combinato-rial problem, which enables us to adopt graph theoreticaltechniques. In this talk, we will present our formulations,algorithms, and experimental results.

Chao YangLawrence Berkeley National LabCYang@lbl.gov

Ali PinarLawrence Berkeley Labapinar@lbl.gov

Juan C. MezaLawrence Berkeley National LaboratoryJCMeza@lbl.gov

Vaibhav DondeEnvironmental Energy Technologies DivisionLawrence Berkeley National Laboratoryvdonde@lbl.gov

Bernard LesieutreLBNLBCLesieutre@lbl.gov

120 CS07 Abstracts

MS51

Optimization for Wave Propagation Problems:From the Design of Acoustic Components to Mi-crowave Tomography

We consider several different optimization problems thatinvolve waves interacting with geometric details of dimen-sions comparable with the wavelength. One example con-cerns the design of devices that efficiently transmit andfavorably distribute acoustic energy in the far field, suchas acoustic horns designed using shape optimization tech-niques, or more general acoustic labyrinths designed uti-lizing topology optimization methods. A second exampleconcerns microwave tomography, that is, the reconstruc-tion of illuminated objects permittivity distribution.

Martin BerggrenDepartment of Information Technology, UppsalaUniversity,The Swedish Defence Research Agencymartin.berggren@it.uu.se

Rajitha Udawalpola, Eddie WadbroDepartment of Information TechnologyUppsala Universityrajitha.udawalpola@it.uu.se, eddie.wadbro@it.uu.se

MS51

Hamilton-Jacobi Equations in Infinite Dimensionfor Approximation of Optimal Design and Recon-struction Problems

Many inverse problems, e.g. in optimal design and recon-struction, can be formulated as optimal control problems.Optimal control problems for low, d, dimensional differ-ential equations, can be solved computationally by theircorresponding Hamilton-Jacobi-Bellman partial differen-tial equation in Rd+1. We will show how to use Hamilton-Jacobi equations in infinite dimension to regularize andsolve optimal design problems for partial differential equa-tions.

Anders SzepessyDepartment of Numerical Analysis and Computer ScienceRoyal Institute of Technology, Stockholmszepessy@kth.se

Mattias SandbergDepartment of MathematicsRoyal Institute of Technology, Stockholmmsandb@kth.se

Jesper CarlssonDepartment of Numerical Analysis and Computer ScienceRoyal Institute of Technology, Stockholmjesperc@kth.se

MS51

Musical Wind Instrument Design: TransmissionLine Analogy And Shape Optimization

Musical wind instrument design is an interesting exampleof a PDE constrained optimization problem. This workpresents how gradient based shape optimization schemesare used to improve the function of brasswinds. Theirshape is described by a large number of degrees of free-dom, and different techniques are presented in order tocomply with visual and manufactural geometrical prefer-ences. A transmission line analogy is employed where ap-

plicable with respect to the solution of the PDE.

Daniel NorelandLaboratoire de Mecanique et dAcoustiqueAix-Marseille Universitenoreland@lma.cnrs-mrs.fr

MS51

Design of Composite Structures with Optimal Fo-cusing Properties

In this talk, we study the problem of designing a flat lens,which focuses a monochromatic wave emanating from apoint source on one side, to a well localized spot on theother side. The lens is realized as a periodic compositestructure, which emerges as a solution to a well-definedoptimization problem. This problem is motivated by therecent intense interest in so-called ”superlenses”, which at-tempt to accomplish the same task using left-handed ma-terials.

Lyubima SimeonovaUniversity of Utahsimeonov@math.utah.edu

David DobsonDepartment of MathematicsUniversity of Utahdobson@math.utah.edu

MS52

Not Available at Time of Publication

To Be AnnouncedTBAtba@tba.edu

MS52

The Structure and Dynamics of the RibosomeStudied by Cryo-EM and Computer Image Pro-cessing: Molecular Mechanism of Translocation

My research involved using cryo-electron microscopy andcomputer image processing to study the structure and dy-namics of the ribosome during translation. I obtained a 3Dreconstruction of the ribosome with the antibiotic fusidicacid. Fusidic acid stops translocation after GTP hydrolysisby preventing the dissociation of EF2. This reconstructionwill be compared with other ribosomal complexes with dif-ferent inhibitors that stop translocation at different stepsto see how translation works.

Krupa DesaiWofford CollegeDesaiKD@Wofford.Edu

MS52

A Thermal Model of the Crust of Saturn’s SatelliteEnceladus

The icy terrain of the Saturnian moon, Enceladus, sug-gests a violent history of bombardment–a history which isactively overwritten by geological mechanisms. Thermalimaging of the southern polar region suggests heat flowsbeneath the ice may be responsible. Furthermore, an early2006 flyby of NASA’s Cassini spacecraft imaged water icejetting from Enceladus’ south pole. We investigate the

CS07 Abstracts 121

effects of these suggested heat flows by modeling the thick-ness of Enceladus surface ice layer.

David Kincaid, Joseph Kane, Steven Henke, Carolyn OttoUniveristy of Wisconsin - Eau Clairekincaidt@uwec.edu, tba@uwec.edu, tba@uwec.edu,tba@uwec.edu

MS52

A Nodal Spectral Element Method Using Curl-conforming Vector Basis Functions on Tetrahedra

Nedelec basis functions are commonly used in the finiteelement method (FEM) solution of electromagnetic fieldproblems. Higher-order finite and spectral elements areclassified as either hierarchical (modal) or interpolatory(nodal). Here we use the Vandermonde matrix to expressthe interpolatory vector basis in terms of a hierarchical ba-sis utilizing the scalar orthonormal polynomials on tetrahe-dra. In an effort to increase efficiency, integration and dif-ferentiation operations are developed using matrix-matrixmultiplications.

Xi LinUniveristy of Illinois at Urbana-Champaignxilin@uiuc.edu

MS52

Plume Containment Using Particle Swarm Opti-mization

We will describe an optimal design problem from water re-sources management. The goal is to design a well-field thatalters the groundwater flow to control the migration of acontaminant plume. The resulting problem is a simulationbased optimization problem where gradient information isunavailable. We solve the problem using particle swarm op-timization (PSO) and point the way towards future work.

Matthew ParnoClarkson Univeristyparnomd@clarkson.edu

MS53

What Can the Theory of Radiation Boundary Con-ditions Contribute to a Theory of Multi-PhysicsInterfaces?

In the past decade there have been substantial practicaladvances in the imposition of radiation boundary condi-tions for the standard models of linear wave propagation.These include fast, low-memory methods for evaluating ex-act nonlocal conditions, improved implementations of localboundary condition sequences, and absorbing layers withreflectionless interfaces. In this talk we will examine the ex-tension of these techniques to more complex interfaces sep-arating regions where different physical models are solved.

Thomas M. HagstromUniversity of New MexicoDepartment of Mathematicshagstrom@math.unm.edu

MS53

Interface Tracking Using Face Offsetting andAnisotropic Mesh Adaptation

Moving interfaces arise in many applications, such as mul-

tiphase flows and fluid-solid interactions. A surface trian-gulation is frequently used to represent the interface, pos-ing significant challenges in interface tracking and meshadaptation. We present a new method for moving inter-faces, called face offsetting, and an anisotropic mesh adap-tation technique to meet these challenges, based on a uni-fied asymptotic and singularity analysis. We report ap-plications of our methods in multi-physics simulations ofsolid-rocket combustion.

Xiangmin JiaoCollege of Computing, Georgia Institute of TechnologyGeorgia Institute of Technologyjiao@cc.gatech.edu

MS53

Algorithms for Shock Wave Propagation in Cou-pled Fluid/Solid Environments

Finite volume methods using Riemann solvers are conve-nient for solving wave propagation problems in heteroge-neous media. If material interfaces align with cell bound-aries then each grid cell contains a distinct material and theRiemann solver resolves jumps into appropriate waves ineach medium. I will discuss application of this approach toshock wave propagation near fluid/solid boundaries wherecompressible fluid equations are coupled to nonlinear elas-ticity, with particular application to the study of shockwave therapy in medical applications. I will also discussCartesian grid approaches to problems with geometricallycomplex interfaces that cut through grid cells so that somecells contain a mixture of materials.

Randall J. LeVequeApplied MathematicsUniversity of Washington (Seattle)rjl@amath.washington.edu

MS53

Back and Forth Error Compensation and Correc-tion for Advections with Applications to Interfaceand Fluid Simulations

Level set method uses a level set function, usually an ap-proximate signed distance function, Phi, to represent theinterface as the zero set of Phi. When Phi is advanced tothe next time level by a transportation equation, its newzero level set will represent the new interface position. Weupdate the level set function Phi forward in time and thenbackward to get another copy of the level set function, sayPhi1. Phi1 and Phi should have been equal if there wereno numerical error. Therefore Phi-Phi1 provides us theinformation of error and this information can be used tocompensate Phi before updating Phi forward again in time.One nice property is that it has the convenience of possiblyimproving the temporal and spatial order of an odd orderscheme simultaneously. We found that when applying thisidea to semi-Lagrangian schemes, e.g., CIR scheme(whichhas no CFL restriction, a nice feature for local refinement),the property is still valid. This technique coupled with asimple yet less diffusive redistancing technique producesa very efficient algorithm even for unstructured trianglemeshes. Numerical results for interface movements withlevel set equation computed by the new method will bepresented in the talk. Also we would like show some inter-esting theoretical results for applying this idea to a generallinear scheme. Further more, the application of this algo-rithm to semi-Lagrangian velocity advection in the NavierStokes’ fluid simulation has greatly reduced the advection

122 CS07 Abstracts

diffusion while essentially keeping the compactness andsimplicity of a first order semi-Lagrangian scheme. Col-laborators: Todd F. Dupont, ByungMoon Kim, IgnacioLlamas and Jarek Rossignac.

Yingjie LiuSchool of Mathematics, Georgia Inst of Techyingjie@math.gatech.edu

MS54

Mobile Actuator Networks for Distributed Feed-back Control of Diffusion Process Using MultiscaleCentral Voronoi Tessellations

In this paper, we address the problem of path planningfor a group of networked mobile robots (sprayers) whichcan release neutralizing chemicals, known as mobile actu-ator networks, to neutralize the toxic 2D diffusion processmodeled by an unknown parabolic distributed parametersystem. We assume that static mesh sensors can informthe networked mobile sprayers the local concentration level.The desired trajectory of the robot is decided by CentroidalVoronoi Tessellations (CVT). Although the collision avoid-ance among the mobile sprayers is automatically build-indue to CVTs, the potential field method is embedded inthe CVT for the mobile robots to avoid dynamic obstaclesin its working space. In addition, since each mobile sprayercan only carry limited amount of neutralizing agent, we in-vestigate the advantage of using multiscale CVT that candynamically group more than one mobile sprayers withinone Voronoi cell when the concentration is high. Simula-tion results are presented to illustrate the proposed solutionto the hard smart spraying problem.

Yangquan Chen, Wei Ren, Haiyang ChaoUtah State Universityyqchen@ece.usu.edu, wren@engineering.usu.edu,chao@cc.usu.edu

MS54

Optimal and Anisotropic CVTs and Their Appli-cations

In this talk, we discuss some recent works on the optimaland nisotropic centroidal Voronoi tessellations (CVTs).The optimal CVTs are related to the Gersho’s conjecture.The anisotropic CVTs are associated with given Riemannmetric tensors and they are defined in a novel way viadirectional distance functions. We present algorithms forthe construction of such CVTs and discuss their variousapplications such as 3d and surface meshing and optimalclustering.

Qiang DuPenn State UniversityDepartment of Mathematicsqdu@math.psu.edu

MS54

Multidimensional Energy-Based Multilevel Quan-tization Scheme and its Applications

We present a multidimensional generalization of the re-cently introduced optimization based multilevel algorithmfor the numerical computation of the centroidal Voronoitessellations. Rigorous proof of the uniform convergenceof the one-dimensional method has been obtained and ithas been conjectured that the scheme would preserve itssuperior numerical properties when extended to higher di-

mensional domains. We build a generalized multidimen-sional algorithm by means of barycentric coordinate basedinterpolation and maximal independent set coarsening pro-cedure. The uniform convergence is demonstrated for avariety of two-dimensional examples with arbitrary densi-ties, guaranteeing a significant speedup when the numberof variables increases. Taking image analysis and quantiza-tion applications as particular examples, we show that themethod can handle large sets of data for both discrete andcontinuous densities and gives significant time reductionand attains better quality of limiting solutions comparingto the commonly used methods.

Maria EmelianenkoDept. of Mathematical SciencesCarnegie Mellon Universitymasha@cmu.edu

Ludmil ZikatanovPennsylvania State Universityludmil@psu.edu

Qiang DuPenn State UniversityDepartment of Mathematicsqdu@math.psu.edu

MS54

An Adaptive Strategy for Convection DominatedProblems with Anisotropic Mesh Refinement

A new numerical approach to solve convection dominatedproblems is proposed. The goal is to design an adaptivealgorithm which utilizes three main ingredients: a stabi-lization method, a reliable and efficient a posteriori er-ror estimator, and an adapted metric tensor to align theanisotropic mesh with the computed solution. Due to thepresence of layers in the solution, the stabilization schemeis necessary to reduce discretization errors and to improveconvergence of the iterative solver. The a posteriori errorestimator is used for estimating the local errors so thatadaptive mesh refinement can be controlled. The meshrefinement turns out to satisfy the alignment and equidis-tribution conditions which can be guaranteed by the opti-mal metric tensor and the anisotropic centroidal Voronoi/Delaunay mesh generator.

Max GunzburgerFlorida State UniversitySchool for Computational Sciencesgunzburg@scs.fsu.edu

Lili JuUniversity of South CarolinaDepartment of Mathematicsju@math.sc.edu

Hoa NguyenSchool of Computational ScienceFlorida State Universitynguyen@scs.fsu.edu

John BurkardtSchool of Computational ScienceFlorida State Universityburkardt@scs.fsu.edu

CS07 Abstracts 123

MS54

Using Spherical Centroidal Voronoi Tessellations inClimate System Modeling

Spherical Centroidal Voronoi Tessellations (SCVTs) offergreat potential to improve our climate system model simu-lations. Unfortunately, only a fraction of this potential hasbeen exploited to date. In the initial search for point setsthat span the surface of the sphere, emphasis was placedon uniformity in terms of cell area and distance betweencell centers. This emphasis on uniformity arose from prob-lems encountered on latitude-longitude grids in the regionof the grid poles. The Voronoi point sets have been highlysuccessful in this regard, and applications involving atmo-spheric modeling, ocean modeling, and sea-ice modelingwill be presented. When we seek uniformity in our Vononoipoint sets on the sphere, the centroidal Voronoi point setsare not substantially different than other Voronoi pointsets, such as those generated on the sphere through recur-sive bisection of the inscribed icosahedron. The powerfulaspect of centroidal Voronoi points sets is their ability toproduce variable resolution grids that maintain a high de-gree of local uniformity. This is precisely the aspect thathas yet to be exploited in climate system modeling. It is of-ten the case in climate system modeling that the importantlength scale of interest varies substantially throughout thedomain, often by an order of magnitude or more in terms ofspacing between generators. Examples will be provided todemonstrate that SCVTs do an exceptional job in allowingus to place resolution where we need it, while at the sametime producing a locally uniform grid. Potential applica-tions of variable-resolution SCVTs to land-ice, sea-ice, andocean modeling will be presented.

Todd RinglerLos Alamos National Laboratoryringler@lanl.gov

MS55

Title Not Available at Time of Publication

Abstract not available at time of publication.

James GeeUniversity of PennsylvaniaDepartment of Radiologygee@mail.med.upenn.edu

MS55

Primal-Dual Techniques in Image Restoration

This talk focuses on TV-regularization in image restora-tion. Based on the Fenchel-duality claculus we introducethe predual of the TV-problem, which turns out to bea bound constrained minimization problem in a Hilbertspace. Then an active-set-type algorithm is introduced andanalysed for the numerical solution of the predual. Thetalk ends by a report on numerical tests.

Michael HintermullerUniversity of GrazDepartment of Mathemathics and Scientific Computingmichael.hintermueller@uni-graz.at

MS55

Segmentation Under Occlusions Using Prior ShapeInformation

Here, we address the problem of segmenting multiple ob-

jects, with possible occlusions, in a variational setting. Tohandle occlusions, we use prior shape information of ob-jects to fill in missing boundary information in overlappingregions. A novelty in our approach is that prior shape isintroduced in a selective manner, only to occluded bound-aries. Further, a direct application of our framework is thatit solves the segmentation with depth problem for certainclasses of images.

Tony F. ChanNational Science Foundationtfchan@nsf.gov

Sheshadri ThiruvenkadamUniversity of California, Los Angelessheshad@math.ucla.edu

MS55

Volumetric MRI Brain Segmentation Using a Mul-tilayer Surface Evolution Approach

This talk will present a novel multilayer level set approachfor the segmentation of anatomical structures in 3D MRIdata. In particular, a nested structure of evolving sur-faces represented by a single implicit function will be usedto segment and classify the white matter, gray matter andcerebro-spinal fluid. Experimental results with prior (prob-abilistic atlas based) and without prior will be presented,together with comparison and validation. This work is sup-ported by the Center for Computational Biology, UCLA.

Arthur TogaUCLALaboratory of Neuro Imagingtoga@loni.ucla.edu

Ivo D. DinovUCLACenter for Computational Biologyivo.dinov@loni.ucla.edu

Ginmo ChungDepartment of MathematicsUCLAsenninha@math.ucla.edu

Luminita A. VeseUniversity of California, Los AngelesDepartment of Mathematicslvese@math.ucla.edu

MS56

A Krylov-Based Descent Algorithm for Optimal H2Model Reduction

In this work, we introduce a Krylov-based descent algo-rithm for optimal H2 approximation of large-scale dynam-icals systems where the interpolation points are the vari-ables of the underlying optimization problem. After deriv-ing the gradient and Hessian of the H2 cost function withrespect to interpolation points, a numerically effective opti-mal H2 model reduction method is developed. Convergenceproperties and effectiveness of the algorithm are presentedthrough numerical examples.

Chris BeattieVirginia Techbeattie@vt.edu

124 CS07 Abstracts

Serkan GugercinVirginia Tech.gugercin@calvin.math.vt.edu

MS56

Adaptive Concepts in Reduced Order Modelling

Proper orthogonal decomposition (POD) is proposed forderiving low order models of large scale dynamical systems.These low order models serve as surrogates for the dynam-ical system in the optimization processes. In the context ofpde constrained optimal control this approach may sufferfrom the fact that the POD basis elements are computedfrom reference trajectories containing features which aredifferent from those of the optimally controlled trajectory.Adaptive POD concepts are discussed which avoid theseshortcomings.

Michael HinzeUniversitat Hamburgmailto:michael.hinze@uni-hamburg.de

MS56

Reduced Order Models and Optimization Methods

Abstract not available at time of publication.

Ekkehard W. SachsUniversity of TrierVirginia Techsachs@uni-trier.de

MS56

Model-Constrained Methods for Reduction ofLarge-Scale Systems

For large-scale optimal design, optimal control, and inverseproblem applications, a key challenge is deriving reducedmodels to capture variation over a parametric input space,which, for many optimization applications, is of high di-mension. This talk presents recent methodology devel-opments in which the task of determining a suitable re-duced basis is formulated as a sequence of optimizationproblems. The methodology is demonstrated for a steadydesign problem, an unsteady turbomachinery probabilisticanalysis problem, and a large-scale contaminant transportinverse problem.

Judy Hill, Bart G. Van Bloemen WaandersSandia National Laboratoriesjhill@sandia.gov, bartv@sandia.gov

Omar GhattasUniversity of Texas at Austinomar@ices.utexas.edu

Karen E. Willcox, Tan Bui-Thanh, Omar BashirMITkwillcox@MIT.EDU, tanbui@mit.edu, bashir@mit.edu

MS57

PCA and Consensus Ensemble Clustering to Strat-ify Breast Cancer into Clinically Useful Subtypes

We describe a technique to integrate principal componentanalysis and consensus ensemble clustering to identify theoptimum cancer subtypes from gene microarray data. Ap-

plied to a breast cancer dataset, we find that it stratifiesinto eight subtypes with distinct molecular signatures, clin-ical course and prognosis. A novel discovery is the iden-tification of two subtypes of primary Her2+ tumors withdifferent natural survival rates. The low recurrence (lowmetastasis) tumors are marked by a strong up-regulationof immunoglobulin genes. These predictions were validatedon unseen data.

Gabriela AlexeMIT and Harvard Universitygabriela.alexe@gmail.com

MS57

Correlations in Complex Disease Association Stud-ies

Association studies for complex disease phenotypes, suchas cell apoptosis rates and age of onset of cancer, en-tail multiple hypotheses testing with many combinationsof single nucleotide polymorphisms. However, these testsare usually far from independent because linkage disequi-librium across the genome induces strong correlations be-tween loci. The problem is compounded by correlationsbetween combinations of distant loci. A mathematical for-malism is developed that correctly accounts for correlationsamongst null association tests by explicitly evaluating themulti-information among polymorphisms. This permits aneffective evaluation of synergistic or antagonistic geneticinteractions with respect to the phenotype.

Gurinder S. AtwalInstitute for Advanced Studiesatwal@ias.edu

MS57

Correlating Mitochondrial SNPs and Complex Dis-ease Phenotypes.

Using complete mtDNA sequences from 672 unrelatedJapanese individuals stratified into seven phenotypes: Di-abetics with Angiopathy, Normal Diabetics, Healthy Non-Obese, Obese Normal, Alzheimer patients, Parkinson pa-tients and Centenarians we describe methods to find cor-relations between phenotype, mtDNA mutations and hap-logroups. Using t-tests, clustering methods and exhaustivepattern searches, we identify sets of mutations correlatedwith the phenotypes. We find that individuals in certainhaplogroups are protected against diabetes and others areselected for longevity. We discuss and apply methods toidentify the causative mechanisms and the time of occur-rence of the mutational events responsible for these effects.

Gyan V. BhanotProfessor, BioMaPS and Biomedical EngineeringRutgers University, Piscataway, NJ 08854gyanbhanot@gmail.com

MS57

Finding Optimum Viral Vaccine Targets for HIVand Avian Flu

HLA polymorphism and high mutation rates make it dif-ficult to create effective viral vaccines. We describe a ge-nomic scanning method across candidate peptides that cre-ates a large number of epitopes per HLA and optimizes thevaccine to prevent viral escape by mutations. We computepeptide cleavage probability and transfer through TAP andMHC binding for many HLA alleles to prune out poorly

CS07 Abstracts 125

conserved and similar-to-self peptides. We then create anoptimal vaccine ordered for cleavage using a genetic al-gorithm. Application of our method to HCV, HIV-I, In-fluenza H3N2 and the Avian Flu Virus will be presented.

Yoram LouzounProfessor, Dept. of Mathematics, Bar Ilan University,Israelylouzoun@gmail.com

MS58

Optimizing Tetrahedral Element Quality UsingOutput from Black-Box Mesh Generators andMesh Smoothing Techniques

An algorithm for rapid, large-scale mesh generation willbe presented in the context of studying near-surface phe-nomena. This procedure takes advantage of open-source(black-box) mesh generation software, and a post-process,mesh-smoothing technique to ensure quality elements inthe final tetrahedral mesh. The result is an optimizationproblem with possibly 100k or more degrees of freedom.The entire procedure will be presented with a specific focuson the smoothing algorithm and the treatment of buriedobjects.

Owen J. EslingerUS Army Corps of EngineersInformation Technology LaboratoryOwen.J.Eslinger@erdc.usace.army.mil

MS58

Parameter Estimation for Large-scale Groundwa-ter Problems

The Engineer Research and Development Center modelsgroundwater flow and transport for monitoring and reme-diation purposes. Data provided for these sites such asborehole data, head values, and concentration values arespatially sparse. Physics based models for some of thesesites are very large and require parallel computer resources.Optimization techniques for these parallel numerical mod-els will be presented that utilize the sparse data to providethe best estimates of the model input parameters.

Jackie P. HallbergU.S. Army Corps of EngineersJackie.P.Hallberg@erdc.usace.army.mil

MS58

Calibration of Ground Water Models with POD

We present some preliminary results which apply themethod of proper orthogonal decomposition (POD) to anelliptic parameter identification problem which arises in thecalibration of ground water models. We generate the PODbasis from the sensitivities taken from a small number offine-scale nonlinear iterations. We solve the nonlinear leastsquares problems at both the fine and reduced scales witha variant of pseudo-transient continuation.

Dan SorensenRice Universitysorensen@rice.edu

Jill Reese, Corey WintonNorth Carolina State Universityjpreese@unity.ncsu.edu, corey.winton@gmail.com

Tim KelleyNorth Carolina State UnivDepartment of Mathematicstim kelley@ncsu.edu

MS58

Heuristic Optimization and Algorithm Tuning Ap-plied to Sorptive Barrier Design

While heuristic optimization is applied in environmen-tal applications, ad-hoc algorithm configuration is typical.We use a multi-layer sorptive barrier design problem as abenchmark for an algorithm-tuning procedure, as appliedto three heuristics (genetic algorithms, simulated anneal-ing, and particle swarm optimization). Design problemswere formulated as combinatorial optimizations where thesorptive layers of a landfill liner were selected to minimizecontaminant transport. Results indicate that formal pre-tuning can improve algorithm performance and provide in-sight into the physical processes that control environmentalsystems.

Alan RabideauUniversity at BuffaloDepartment of Civil, Structural, and EnvironmentalEngineerirabideau@buffalo.edu

Shawn MatottEnvironmental Protection Agencylsmatott@buffalo.edu

Shannon Bartelt-HuntUniversity of Nebraska-Lincolnsbartelt@mail.unomaha.edu

Kathleen FowlerClarkson Universitykfowler@clarkson.edu

MS59

Numerical Methods for Boundary Value Problemsin Stochastic Domains

Efficient methods for the numerical realization of ellipticPDEs in domains depending on random variables are pre-sented. Mappings or Fictitious Domain techniques are usedto handle the domain randomness. Generalized Wiener ex-pansions are invoked to convert such stochastic problemsinto deterministic ones, depending on an extra set of realvariables (the stochastic variables). Discretization is ac-complished by finite elements in the physical variables andG-NI (Galerkin projection with numerical integration) inthe stochastic variables.

Claudio CanutoPolitecnico di Torinoclaudio.canuto@polito.it

MS59

Finite Element Methods for Stochastic ParabolicPDEs in High Dimensions

Abstract not available at time of publication.

Yanzhao CaoDepartment of mathematics,Florida A&M University, Tallahassee, FL32307

126 CS07 Abstracts

yanzhao.cao@famu.edu

MS59

Stochastic Galerkin and Stochastic Collocation forSPDEs

We will discuss Stochastic Galerkin and Stochastic Collo-cation methods combined with sparse approximation tech-niques as alternatives to the classical Monte Carlo ap-proach for the approximation of SPDEs. The mathemat-ical analysis of these methods and the characterization oftheir convergence is extremely relevant to decide in whichcases they should be used. We will present novel results,discussing the efficient implementation and the mathemat-ical analysis of the different sources of approximation errorin the numerical solutions.

Clayton G. WebsterFlorida State Universitywebster@scs.fsu.edu

Raul TemponeSchool of Computational Science and MathematicsDepartmentFlorida State Universityrtempone@scs.fsu.edu

Fabio NobileMOX, Dip. di MatematicaPolitecnico di Milanofabio.nobile@polimi.it

MS59

An Adaptive Multi-Element Generalized Polyno-mial Chaos Method for Elliptic Problems withRandom Coefficients

We develop an adaptive multi-element generalized polyno-mial chaos (ME-gPC) method for elliptic equations withrandom coefficients of a moderate number (≤ 10) of ran-dom dimensions, where we employ low-order polynomialchaos (p ≤ 3) and refine the solution adaptively in the ran-dom space. We generate local and global a-posterior errorestimators. To reduce to the cost of solving the error equa-tions, we construct a reduced space, where a much smallernumber of terms in the enhanced polynomial chaos spaceare used to capture the errors.

Xiaoliang WanBrown University, Division of Applied Mathxlwan@dam.brown.edu

George KarniadakisBrown Universitygk@dam.brown.edu

MS60

The Synergy of Computer Science and ScientificComputing

Scientific computing and computer science have a longsymbiotic history which is perhaps not easily perceivedsince most problems of computer science are discrete asopposed to the continuous aspect of numerical analysis.However, the use of topics such as combinatorics, compilerdesign, datamining, etc, are being increasingly prevalentin scientific computing. This presentation will review howsome of these areas are being applied to improve and ex-

tend numerical techniques and software.

Sanjukta BhowmickDepartment of Applied Physics and Applied MathematicsColumbia Universitybhowmick@cse.psu.edu

MS60

A Self-Adapting System for Linear Solver Selection

A self-adapting system integrates several components: fea-ture extraction, a database for storage of features andruntime results, a modeller that builds recommendationstrategies from the information in the database, and a run-time recommender. We will describe the general ideas ofthe SALSA system, and its implementation, in particularthe statistical and machine learning techniques used for therecommender component.

Victor EijkhoutThe University of Texas at AustinTexas Advanced Computing Centereijkhout@tacc.utexas.edu

Erika FuentesUniversity of Tennesseeefuentes@cs.utk.edu

MS60

Enabling Adaptive Algorithms in Component Ap-plications

Component-based software engineering has been gainingpopularity in scientific computing, facilitating the cre-ation and management of large multi-disciplinary, multi-developer application codes, and providing opportunitiesfor improved performance and numerical accuracy by en-abling selection among multiple solution approaches. Wepresent a component infrastructure for the support of dy-namic algorithm selection and adaptation in applicationsinvolving the solution of nonlinear PDEs. We also describea general architecture for providing quality of service fornumerical software in component-based environments.

Lois McInnesArgonne National Laboratorycurfman@mcs.anl.gov

Sanjukta BhowmickDepartment of Applied Physics and Applied MathematicsColumbia Universitybhowmick@cse.psu.edu

Boyana NorrisArgonne National LaboratoryMathematics and Computer Science Divisionnorris@mcs.anl.gov

Dinesh K. KaushikArgonne National LaboratoryD-247, Bldg. 221, MCS Divkaushik@mcs.anl.gov

MS60

Domain-Specific Program Analysis with Open-Analysis

Program analysis is necessary in many application domains

CS07 Abstracts 127

including software engineering, high performance comput-ing, scientific computing, data mining, and operating sys-tems. However, reusing analysis implementations is diffi-cult because they are typically coupled to a particular in-termediate representation (IR). The OpenAnalysis toolkitseparates analysis from the intermediate representation ofthe program. In this talk I will present some of the re-search questions involved in automating the generation ofdomain-specific, data-flow analysis implementations.

Michelle StroutComputer Science Department,Colorado State Universitymstrout@cs.colostate.edu

MS61

An Extensible Framework for the MathematicalManipulation of Music

The goal of this project was the creation of an extensiblesound manipulation architecture using Mathematica. Thetwo essential phases were the implementation of a structureto play sounds, and a system for the exploration of granularsynthesis. The first phase includes functions for the basicimplementation of a song. The more important granularsynthesis phase consists of functions for the engineeringand of sound clouds, collections of thousands of very shortenveloped waveforms (sound grains).

Elom AbaloWofford CollegeAbaloEK@Wofford.Edu

MS61

Talk Title Not Available at Time of Publication

To Be AnnouncedTBAtba@tba.edu

MS61

Using COMSOL to Develop a HydrodynamicModel of the Chesapeake Bay

This talk displays results from using COMSOL to develop ahydrodynamic model of the Chesapeake Bay. The model it-self was initially divided into two separate sets of problems.The first deals with running the non-linear Navier-Stokesequations in simple rectangular geometries. The other halfof the project solves linear PDEs in the complete geometryof the Chesapeake. When the two halves of the projectare completed, they are combined together, creating a fullnon-linear model.

Madeline BowUnited States Naval Academym070588@usna.edu

MS61

Hydrocode Simulations of Impacts in the Outer So-lar System

Imaging of the icy surfaces of outer solar system bodies bythe Voyager, Galileo and Cassini missions reveals an ex-tensive history of bombardment, predominantly by comets.To analyze the physics of such events, a Smoothed ParticleHydrodynamics (SPH) model was used to simulate the im-pact of a comet on an icy surface. One focus of this study

was the extent of pyrolysis of pre-existing organic materialin the icy target resulting from the impact shock.

Steven HenkeUniversity of Wisconsin - Eau Clairehenkesf@uwec.edu

MS61

Spectral Collocation for Resolving Spike Dynamics

In this work the Gierer-Meinhardt model is analyzed usingChebyshev collocation methods. This reaction-diffusionsystem is governed by activator and inhibitor concentra-tions. Initially, the system is considered in one dimensionand then in two dimensions; numerical results are pre-sented for both cases. The algorithmic complexity andaccuracy are compared to a moving finite element method.Finally, observations are made concerning when to use theproposed spectral method as opposed to the establishedmoving mesh method.

Michael McCourtIllinois Institute of Technologymccomic@iit.edu

MS62

Simulating Potential Hydrogen Explosions in Nu-clear Reactor Containment Buildings

We describe the use of a high resolution finite method basedwave propagation algorithms for simulating potential hy-drogen explosions in nuclear reactor containment buildings.In this work, the reactive Euler equations are solved onan adaptively refined, mapped grid representing the con-tainment building. The flame front is modeled using eitherlevel set like approach for deflagration, or an Arrhenius lawfor detonations. Peak over-pressures and impulses on thecontainment structure are sought, along with peak tem-peratures inside the structure. A general equation of statemodeling the dependence of specific heats on temperaturemay be used.

Donna CalhounCommissariat a l’energie Atomiquedonna@semt2.smts.cea.fr

MS62

A Wave Propagation Analysis of the October 2,2004 Tremor at Mount St. Helens, Washington

On October 2, 2004, three component, broad-frequencyband seismometers detected a prominent low-frequencyresonance within Mount St. Helens associated with theonset of eruptive volcanic activity. The energy is domi-nantly in the 0.5 to 10 Hz range. I test the idea that thissignal is generated by sudden extension of a long, visco-elastic magma body as it forces its way through a brittlecrust using the finite volume method of Leveque (2002).

Roger P. DenlingerU.S. Geological Survey,roger@usgs.gov

MS62

Finite Volume Methods and Adaptive Refinementfor Global Tsunami Propagation and Local Inun-

128 CS07 Abstracts

dation

Modeling global tsunami propagation as well as inundationrequires resolving diverse flow regimes and spatial scaleswith a single numerical method. The shallow water equa-tions, a commonly accepted governing system, are a set ofhyperbolic conservation laws—demanding specialized nu-merical methods. I will describe the extension of a class offinite volume methods developed for such systems, as wellas unique modifications and attributes necessary for usingthese methods for tsunami modeling.

David L. GeorgeDepartment of MathematicsUniversity of Utahgeorge@math.utah.edu

MS62

Numerical Models for the Interaction of VolcanicFlows with Water

Modeling a pyroclastic surge interacting with a body ofwater requires a coupling of compressible gas dynamics fora hot dusty gas with fluid equations for the liquid, ideallyincluding heat transfer and phase change as well as pen-etration of the water by the solid phase. An approach tothis problem well be presented based on high resolutionwave propagation algorithms for a dusty gas developed byPelanti and LeVeque and previously used to model volcanicjets and plumes.

Kyle T. MandliUniversity of WashingtonDept. of Applied Mathematicsmandli@amath.washington.edu

MS63

Aspects of Unstructured Finite Volume Methodand Optimal Design in the European Project ”NewAircraft Concepts Research” (NACRE)

Gradient-based aerodynamic shape optimization based onComputational Fluid Dynamic is used in the context ofthe European Project ”New Aircraft Concepts Research”(NACRE) in the prospect to speed up the design of newaircrafts. The core of the computer program used here isthe Unstructured Finite Volume solver Edge, which solvesthe flow and adjoint flow equations. Aspects of the gradientcomputation, for example involving the mesh deformationand the pre-processing, will also be presented.

Olivier G. AmoignonFOI-Swedish Defence Research Agencyolivier.amoignon@foi.se

Martin BerggrenDepartment of Information Technology, UppsalaUniversity,The Swedish Defence Research Agencymartin.berggren@it.uu.se

MS63

Modeling Fluid Structure Interactions in Under-water Cavities

Fluid Structure modeling is used to study the occurrenceof Helmholtz resonance due to coupling of the structuraldeflections with the shear layer oscillations in underwatercavities. The method employs an edge based multi-element

finite volume flow solver coupled loosely with a similarlystructured finite volume structural solver. Mesh motion toaccomodate surface deflection is handled by treating themesh as an elastic structure. The details of the solver,coupling methods and some results are presented.

Srinivasan ArunajatesanCombustion Research and Flow Technology, Inc.ajs@craft-tech.com

MS63

An Accurate and Conservative Load TransferScheme for Fluid/Structure Interaction Simula-tions with Non-Matching Interface Discretizations

In aeroelastic simulations, the precision of fluid-inducedload transfer across non-matching fluid/structure inter-faces plays a key role in the accuracy of the coupled scheme.In this work, we compare the performance of a novel loadtransfer scheme based on a common refinement of the dis-cretized interface to state-of-the-art point-to-element loadtransfer schemes. Through a set of fluid/structure prob-lems involving flat and curved interfaces, we quantify thesubstantial improvement in accuracy achieved by the newscheme.

Philippe H. Geubelle, Rajeev Jaiman, Eric LothAerospace Engineering DepartmentUniversity of Illinois at Urbana-Champaigngeubelle@uiuc.edu, jaiman@uiuc.edu, loth@uiuc.edu

Xiangmin JiaoUniversity of Illinois at Urbana-Champaignjiao@cc.gatech.edu

MS63

Multiphase Flow Simulations of Solid-PropellantRockets on Unstructured Grids

A multiphase flow simulation framework for solid-propellant rocket motors is presented. Unstructured gridsare used to enable representation of geometrically com-plex domains. Detailed information is provided about thedroplet-localization algorithm and its parallel implementa-tion. A distinguishing feature of our droplet-localization al-gorithm is that it gathers automatically data about dropletimpacts on boundaries. Results are provided for the AFRLBATES and RSRM motors.

Fady NajjarCenter for Simulation of Advanced RocketsUniversity of Illinois at Urbana-Champaignfnajjar@csar.uiuc.edu

Andreas HaselbacherCSARU. Illinois Urbana-Champaignhaselbac@uiuc.edu

MS63

Aspects of Reconstruction Schemes on Unstruc-tured Mesh Flow Solvers

Data reconstruction techniques used in unstructured meshflow solvers are investigated in the context of gradient lim-ited and flux limited TVD schemes. Of particular concernis reconstruction on meshes containing highly curved largeaspect ratio cells (e.g., boundary layer regions). Gradient

CS07 Abstracts 129

based MUSCL reconstruction is compared to a collinearedge reconstruction that only requires a modest modifi-cation to existing edge data structures. While somewhatrestricted, the collinear edge reconstruction provides im-proved robustness.

Thomas M. SmithSandia National LaboratoriesParallel Computational Sciencetmsmith@sandia.gov

MS64

A Stochastic Immersed Boundary Method Incor-porating Thermal Fluctuations: Toward ModelingFlexible Micromechanics

The mechanics of many physical systems arising in themodeling of biological processes and technological devicesinvolve elastic structures which interact with a fluid. TheImmersed Boundary Method is one approach which hasbeen applied with some success to macroscopic systems,including blood flow in the heart, wave propogation inthe inner ear, and lift generation in insect flight. How-ever, at sufficiently small length scales thermal fluctua-tions become significant and must be taken into account.We shall discuss an extension of the Immersed Bound-ary Method framework which incorporates thermal fluc-tuations through appropriate stochastic forcing terms inthe fluid equations. This gives a system of stiff SPDE’s forwhich standard numerical approaches perform poorly. Wediscuss a novel stochastic numerical method which exploitsstochastic calculus to handle stiff features of the equations.We further show how this numerical method can be ap-plied in practice to model the basic microscopic mechanicsof polymers, polymer knots, membrane sheets, and vesi-cles. We also discuss preliminary work on modeling themicromechanics of cellular structures.

Paul AtzbergerUniversity of California-Santa Barbaraatzberg@math.ucsb.edu

MS64

Operator Splitting for Fluid Flow in DeformableDomains

Fluid flows with free surface and fluid-structure interac-tion problems are examples of fluid flows in deformabledomains. We formulate the flow problem in a refer-ence domain and we use a time discretization by oper-ator splitting to reduce the solution of the original flowproblem to that of simpler sub-problems. We combinethe time-splitting scheme with an isoparametric Bercovier-Pironneau finite element approximation of the Navier-Stokes equations. The wave-like equation methodolog isused to handle the pure advection problems resulting fromthe time-splitting and from the domain transformation.The resulting methodology is modular, relatively easy toimplement, and it introduces very little numerical dissipa-tion.

Giovanna GuidoboniUniversity of HoustonDepartment of Mathematicsgio@math.uh.edu

MS64

A Fictitious Domain Method Based Novel Numer-

ical Scheme for the Viscoelastic Particulate Flow

We present a fictitious domain method based novel numer-ical scheme for the particulate flows in Oldroyd-B fluid bycombining Stokes solvers, a wave-like equation treatmentof the advection, and the rigid body motion projection viaoperator-splitting. The new scheme takes advantage of ma-trix decomposition and guarantees positive definiteness ofthe configuration tensor at all times. The 2D numericalsimulations of sendimentations of a particle and severalparticles in the fluid will be presented.

Jian Hao, Roland GlowinskiUniversity of Houstonjianh@math.uh.edu, roland@math.uh.edu

Tsorng-Whay PanDepartment of MathematicsUniversity of Houstofnpan@math.uh.edu

MS64

Domain Decomposition Method for Wave Propa-gation in Heterogeneous Media

In this talk we address the numerical solution of a waveequation with discontinuous coefficients by a finite elementmethod using domain decomposition and semimatchinggrids. A wave equation with absorbing boundary condi-tions is considered, the coefficients in the equation essen-tially differ in the subdomains. The problem is approxi-mated by an explicit in time finite difference scheme com-bined with a piecewise linear finite element method in thespace variables on a semimatching grid. The matching con-dition on the interface is taken into account by means ofLagrange multipliers. The resulting system of linear equa-tions of the saddle-point form is solved by a conjugate gra-dient method.

Serguei LapinUniversity of Houstonslapin@math.uh.edu

MS64

Two Efficient Projection Methods

The MAC projection method has been a very successfulmethod for solving the Navier-Stokes equations. Its spatialallocation enables achieving the divergence-free conditionexactly, and more importantly ensures numerical stability.On the other hand, the different spatial allocation for eachvelocity component make numerical schemes complicatedespecially with implicit treatment of the visous terms. Weintroduce two novel projection methods that sample all thevelocity component at one location and achieve numericalstability and second order accuracy.

Frederic GibouUC Santa Barbarafgibou@engineering.ucsb.edu

Chohong MinDepartment of MathematicsUniversity of Californiachohong@math.ucsb.edu

130 CS07 Abstracts

MS65

Moderator

Donald EstepColorado State Universityestep@math.colostate.edu

MS66

Application of Averaging-Based Error Estimationto Problems in Adaptive Atmospheric Modeling

Adaptive methods for atmospheric modeling are becomingmore and more popular for simulating phenomena with lo-calized features. In general, adaptive computational meth-ods heavily rely on the quality of criteria to control theadaptation process. So far, most adaptive atmosphericsimulation approaches utilize gradient based heuristical orphysically induced refinement criteria. In this presentationwe report on recent results in the construction of averaging-based rigorous error estimators for adaptive atmosphericsimulation problems. A short introduction of the deriva-tion of such error estimation is given and a comparisonwith common gradient-based methods is shown.

Joern BehrensAlfred-Wegener-Institute for Polar and Marine Researchjbehrens@awi-bremerhaven.de

Lars MentrupTechnische Universitaet Muenchen (M3)Boltzmannstr. 3, 85747 Garching, Germanymentrup@ma.tum.de

MS66

An Adaptive Method with Error Control for High-Order Discontinuous Galerkin Methods Applied toHamilton-Jacobi Equations

We propose and study an adaptive version of the discon-tinuous Galerkin method for Hamilton-Jacobi equationswhich, given a tolerance and the polynomial degree of theapproximate solution, finds a mesh on which the approxi-mate solution has a distance (in the uniform norm) to theviscosity solution no bigger than the prescribed tolerance.Our numerical experiments show that the method achievesits goal with optimal complexity independently of the tol-erance and the polynomial degree.

Bernardo Cockburn, Yanlai ChenSchool of MathematicsUniversity of Minnesotacockburn@math.umn.edu, ylchen@math.umn.edu

MS66

A 3D Self-Adaptive, Goal-Oriented hpFEM with aMultigrid Solver. Applications to Electromagnet-ics

We describe the development of a self-adaptive hp goal-oriented 3D Finite ElementMethod (FEM) applied to thesimulation of borehole resistivity measurements for the as-sessment of rock formation properties. The self-adaptivealgorithm delivers (without any user interaction) a se-quence of optimal hp-grids that converges exponentiallyin terms of a user-prescribed quantity of interest with re-spect to the CPU time. The self-adaptive algorithm iter-ates along the following steps. Given a (coarse) conform-

ing hp mesh, it is first globally refined in both h and p toyield a fine mesh, i.e. each element is broken into eightnew elements, and the discretization order of approxima-tion p is raised uniformly by one. Subsequently, the prob-lem of interest is solved on the fine mesh. The next opti-mal coarse mesh is then determined as the one that max-imizes the decrease of the projection based interpolationerror averaged by the added number of unknowns. Sincethe mesh optimization process is based on the minimiza-tion of the interpolation error rather than the residual, thealgorithm is problem independent, and it can be appliedto different physics (acoustics, elasticity, etc.), nonlinearand eigenvalue problems as well. The fine mesh problemcontains typically 20-30 times more unknowns than the cor-responding coarse mesh problem. Thus, an efficient multi-grid (two grids only) solver of linear equations for hp-finiteelements has been developed. It utilizes a block-Jacobismoother on the fine grid combined with a global solutionon the coarse grid (also called coarse grid correction). Afine grid edge-based overlapping block-Jacobi smoother hasbeen employed to avoid degeneration of convergence prop-erties due to the presence of elongated elements. This two-grid cycle is accelerated by using a goal-oriented steepest-descend method. Numerical results indicate that the itera-tive solver converges typically in less than fifteen iterations,even in presence of elongated elements with an aspect ra-tio up to 100000:1. Visit www.ices.utexas.edu/Pardo fordetails and the most updated progress on this research.

Carlos Torres-VerdinDepartment of Petroleum and Geosystems EngineeringUniversity of Texas at Austincverdin@mail.utexas.edu

David PardoDept. of Petroleum EngineeringUT Austindzubiaur@yahoo.es

Maciek PaszynskiDept. of Computer ScienceAGH University of Science and Technologypaszynsk@agh.edu.pl

Leszek DemkowiczInstitute for Computational Engineering and Sciences(ICES)The University of Texasleszek@ices.utexas.edu

MS66

The Computation of a-Posteriori Bounds for Func-tional Outputs of PDEs Using DiscontinuousGalerkin Methods

We present a formulation to calculate upper and lowerbounds for functional outputs of the exact weak solutionof coercive partial differential equations. It turns out thatwhen using DG formulations most of the necessary ingre-dients required for the computation of bounds are read-ily available and as a consequence, the computation ofbounds results in a minimum overhead. We will presentconvection-diffusion equations at low and high Peclet num-bers, the Stokes equation as well as our initial investigationinto the extension of the approach to the low Reynoldsnumber steady state incompressible Navier-Stokes equa-tions.

Joseph Wong, Jaime Peraire

CS07 Abstracts 131

Massachusetts Institute of Technologybjorn@mit.edu, peraire@MIT.EDU

MS67

Diffuse Interface Methods

We consider diffuse interface methods for modeling andsimulation of fluid interfaces and for problems in image in-painting. We show how to design efficient and fast numeri-cal schemes for such problems and how asymptotic analysiscombined with bifurcation theory can suggest approachesfor efficient topological reconnection in image inpainting.For fluid interfaces we show how such methods can be quan-titatively compared to experimental data.

Andrea L. BertozziUCLA Department of Mathematicsbertozzi@math.ucla.edu

MS67

Modeling and Computing the Blink Cycle in theTear Film

A tear film is left on the front of the eye with each blink.Formation and evolution of the film over multiple blinkcycles is studied using lubrication theory. Different numer-ical methods are implemented and compared on a movingdomain. Comparison of the results with in vivo interfer-ometry for a half blink is favorable. For many conditions,only 7/8 of full lid closure is required to completely restartthe film according to fluid dynamics.

Pamela CookDepartment of Mathematical SciencesUniversity of Delawarecook@math.udel.edu

Alfa HeryudonoUniversity of DelawareDept of Mathematical Sciencesherydon@math.udel.edu

Tobin DriscollUniversity of DelawareMathematical Sciencesdriscoll@math.udel.edu

Richard BraunUniversity of Delaware, Newark, DEDepartment of Mathematical Sciencesbraun@math.udel.edu

Ewen King-SmithCollege of OptometryOhio State Universityeking-smith@optometry.osu.edu

MS67

Modeling and Simulation of Simple Locomotors inStokes Flow

Motivated by the locomotion and modeling of heavilyflagellated micro-organisms and by recent experiments ofchemically driven nanomachines, we study the dynamics ofbodies of simple geometric shape that are propelled by tan-gential surface stresses. For a Stokesian fluid, we have de-veloped a mathematical model of the body dynamics basedon a mixed-type boundary integral formulation. We will

discuss the effect of body geometry on the dynamics, aswell as interactions between multiple bodies.

Michael ShelleyCourant Institute, New York Universityshelley@courant.nyu.edu

Anna-Karin Tornberg, Alex KanevskyCourant Institutetornberg@courant.nyu.edu, kanevsky@cims.nyu.edu

MS67

Shape Optimization of Swimming Sheets

Motivated by the propulsion mechanisms adopted by gas-tropods, we consider shape optimization of a flexible sheetwhich propels itself over a thin layer of viscous fluid bypropagating deformation waves along its body. We use a lu-brication approximation to model the dynamics and derivethe relevant Euler-Lagrange equations to optimize swim-ming speed and efficiency. We present a fast, highly ac-curate method for solving the optimization equations andexplore the solution in various singular limits. We alsomonitor the validity of the model using a new rigorous er-ror estimate for Reynolds’ approximation.

Jon WilkeningUC Berkeley Mathematicswilken@math.berkeley.edu

MS68

Internships and Work Experience in Undergradu-ate CSE Education

An internship or work experience can be the climax of aCSE undergraduate’s education. With exposure to manynew ideas, techniques, and applications at another institu-tion, such an experience can greatly broaden and deepenthe student’s understanding of computational science andmake the classroom education more meaningful. More-over, work with a professional computational science teamand contacts made during the summer can greatly enhanceopportunities and options available to the CSE undergrad-uate.

Angela B. ShifletMathematics and Computer ScienceWofford Collegeshifletab@wofford.edu

MS68

Introduction to the Working Group Report

This presentation will provide an overview of the report onUndergraduate CSE Education and an introduction to theminisymposium. We will begin with our working definitionof CSE, outline the sections and the topics for the presen-tations to follow. Attention will be paid to the differingforms and needs an undergraduate education in CSE cantake and must try to meet.

Peter R. TurnerClarkson UniversityMathematics and Computer Science Departmentpturner@clarkson.edu

MS68

Undergaduate Computational Science and Engi-

132 CS07 Abstracts

neering Programs

The Minisymposium is organized and presented by theworking group on the SIAM report of UndergraduateCS&E education. This presentation will highlight the dif-ferent versions of computational science programs at theundergraduate level. (e.g., B.Sc programs, minor pro-grams, certificate programs, etc). The session will also pro-vide information on educational materials for the teachingand learning of CS&E at the undergraduate level.

Ignatios E. VakalisProfessor of Computer ScienceCalPoly State Univ. San Luis Obispoivakalis@csc.calpoly.edu

MS69

Moderator

Omar GhattasUniversity of Texas at Austinomar@ices.utexas.edu

MS70

Implementation of Flow Solvers in COMSOL Mul-tiphysics: Overview and Demonstration

As computational science progresses, the need for a generalmultiphysics platform (or at least strategy) has becomeevident. A multiphysics framework may not, however, beeasily compatible with the sophisticated discretization andsolution methods required by specialized fields in scienceand engineering, such as incompressible flow. This pre-sentation will give an overview and demonstration of theCOMSOL Multiphysics platform and the challenges asso-ciated with integrating flow solvers into a general multi-physics environment.

David KanCOMSOL, Inc.david.kan@comsol.com

MS70

IFISS: A Matlab Toolbox for Modelling Incom-pressible Flow

IFISS is a MATLAB package for the interactive numeri-cal modelling of incompressible flow problems. It includesalgorithms for discretisation by mixed finite element meth-ods and a posteriori error estimation of the computed so-lutions. It can also be used as a computational laboratoryfor experimenting with state-of-the-art preconditioned it-erative solvers for the discrete linear systems that arisein incompressible flow modelling. Here we will discuss itsmain features and demonstrate its use on some practicalproblems.

Alison RamageUniversity of StrathclydeA.Ramage@strath.ac.uk

MS70

Groundwater Flow Modelling Using the IFISSToolbox

Mixed finite element approximation of the PDEs modellingsteady incompressible flow leads to symmetric indefinite

linear systems of equations. We describe a generic blockpreconditioning technique for such systems based on alge-braic multigrid and describe an implementation in MAT-LAB and COMSOL. Some numerical results are presentedshowing the effectiveness of our approach in the contextof diffusion equations that arise in modelling ground-waterflow in porous media that exhibit random spatial variabil-ity.

Catherine Powell, David SilvesterSchool of MathematicsUniversity of Manchester, Manchester, UKc.powell@manchester.ac.uk, d.silvester@manchester.ac.uk

MS70

Comparing Incompressible Flow Preconditionerswith IFISS

In CFD, there is a strong need for fast and robust itera-tive solvers for the discretized incompressible Navier Stokesequations. Popular methods are preconditioned Krylovsolvers. The most important part is to find a good pre-conditioner. We present a new ILU with reordering pre-conditioner, which is compared with the pressure convec-tion diffusion (PCD), least squares commutator (LSC), andaugmented Lagrangian based (ALB) preconditioners. Wecompare these preconditioners for a number of problemsobtained from the IFISS package.

Mehfooz ur Rehman, Guus Segal, Kees VuikDelft University of Technologym.v.r.rehman@tudelft.nl, a.segal@tudelft.nl,c.vuik@tudelft.nl

MS71

An Overview of the LSMLIB Library: Design andUsage

The Level Set MethodLibrary (LSMLIB) is a C++/C/Fortran/MATLAB soft-ware library that provides support for the serial and paral-lel simulation of implicit surfaces and curves dynamics intwo- and three-dimensions. It is designed to deliver high-performance, level set method algorithms to the applica-tion’s developer while requiring only a high-level under-standing of the level set method formalism. We present anoverview of the LSMLIB software including a few examplesdemonstrating it usage in various modes.

Kevin T. ChuMechanical & Aerospace EngineeringPrinceton Universityktchu@princeton.edu

Masa ProdanovicUniversity of Texas at AustinInstitute for Computational Engineering and Sciencesmasha@ices.utexas.edu

MS71

Surface Area Minimization of Triply-Periodic Sur-faces with Volume Fraction Constraint Via theLevel Set Method

We present a variational level set approach for theoreticallyand computationally studying triply-periodic surfaces thatminimize the total surface area when there is a constrainton the volume fraction of the regions that the surface sepa-

CS07 Abstracts 133

rates. We demonstrate that optimal surfaces are preciselythose possessing constant mean curvature. We then studythe optimality of several well-known minimal surfaces andexplore the properties of optimal surfaces when the vol-ume fractions of the two phases are not equal. ParallelLSMLIB is used to handle the computational cost of thethree-dimensional shape optimization problem.

Kevin T. ChuMechanical & Aerospace EngineeringPrinceton Universityktchu@princeton.edu

Salvatore TorquatoPRISM, Chemistry, PACM, PCTPPrinceton Universitytorquato@electron.princeton.edu

Youngjean JungDepartment of Civil and Environmenal EngineeringDuke Universityyoungjean.jung@duke.edu

MS71

Investigating Spontaneous Capillarity-ControlledEvents Via the Level Set Method

An accurate description of the mechanics of pore level dis-placement of immiscible fluids could significantly improvethe macroscopic parameter predictions from pore networkmodels in real porous media. Assuming quasi-static dis-placement, we describe a simple but robust model basedon the level set method for determining critical events forthroat drainage and pore imbibition. The method arrivesat geometrically correct interfaces while robustly handlingtopology changes and is independent of the pore space com-plexity.

Masa ProdanovicUniversity of Texas at AustinInstitute for Computational Engineering and Sciencesmasha@ices.utexas.edu

Steven L. BryantPetroleum and Geosystems Engineering DepartmentUniversity of Texas at Austinsteven bryant@mail.utexas.edu

MS71

Solving Two-Phase Incompressible Stokes Equa-tions Using the Immersed Interface Method andLSMLIB

Two-phase incompressible Stokes equations appear inmany physical and biological applications. We use thesecond-order Immersed Interface Method (IIM) coupledwith the Level Set Method (LSM) to solve multiphaseStokes flows with singular interface force and piecewise con-stant viscosity coefficient. The Stokes equations are decou-

pled into Poisson equations using the projection method.To use the IIM for the decoupled Poisson equations, we firstderive the jump conditions for both the pressure and thevelocity in the case where the two fluids may have unequalviscosity coefficients. Since the jump conditions for the

kinematic variables can be decoupled by introducing aug-mented variables, we use the Generalized Minimal Resid-

ual (GMRES) method to solve for the augmented variables,and then solve the Stokes equations. The interface between

two fluid phases is implicitly represented using a level setfunction. We couple the LSM with IIM for moving inter-face problems such as mean curvature flows for both 2Dand 3D. Numerical simulations show that our algorithmimplemented using LSMLIB is both efficient and second-order accurate.

Xiaohai WanCapital One Financialxiaohai.wan@capitalone.com

MS72

Local Quasicontinuum-Like Reduction of Opti-mization Problems in Materials Science

We present a local quasicontinuum-like approach for modelreduction of minimum energy problems in materials sci-ence, and we give sufficient conditions for the well-posedness of the reduced problem. The approach includesa recent multiscale model reduction approach for orbital-free density functional theory electronic structure calcula-tions that was proposed by the authors as well as the localquasicontinuum approach for potential-based calculations.Numerical results validate our findings.

Mihai AnitescuArgonne National LaboratoryMathematics and Computer Science Divisionanitescu@mcs.anl.gov

Dan NegrutUniversity of Wisconsin MadisonDepartment of Mechanical Engineeringnegrut@engr.wisc.edu

Peter ZapolArgonne National LaboratoryMaterials Science Divisionzapol@anl.gov

MS72

Algorithms for Inverse Problems Under Uncer-tainty: Applications to Dynamic Data Driven As-similation of Nonlinear Dynamical Systems.

Data driven assimilation algorithms are typically appliedto problems in geophysics and weather prediction. Thekey ideas however, extend to many systems that operateunder uncertainty. In this talk we present a new algo-rithm for data assimilation that is inspired on ensembleKalman filter but is based on algorithms from large-scalePDE-constrained optimization. We apply the new ideasto nonlinear chaotic dynamical systems, first proposed byE.N. Lorenz.

Santha Akella, George BirosUniversity of Pennsylvaniaakella@seas.upenn.edu, biros@seas.upenn.edu

MS72

Multigrid Schemes for Distributed Parameter Es-timation Problems

Distributed parameter estimation problems represent aclass of inverse problems with a bilinear structure. In these

134 CS07 Abstracts

cases, an optimization approach is considered where theinherent ill-posedness of these problems is accommodatedby appropriate regularization and solution techniques. Forthis purpose, the experience gathered with the multigridsolution of singular optimal control problems and with theconcept of strong coupling of optimization variables willbe instrumental for the development of the multilevel al-gorithms presented in this talk. The inherent optimizationand globalization properties of the resulting multigrid pro-cesses will be discussed.

Alfio BorziUniversity of Grazmailto:alfio.borzi@uni-graz.at

MS72

Inexact Adaptive Multilevel Methods for PDE-Constrained Optimization

We present a class of inexact multilevel SQP-methodsfor the efficient solution of PDE-constrained optimizationproblems. The algorithm starts with a coarse discretizationof the underlying optimization problem and provides 1) im-plementable criteria for an adaptive refinement strategy ofthe current discretization and 2) implementable accuracyrequirements for iterative solvers of the PDE and adjointPDE on the current grid such that global convergence tothe solution of the infinite-dimensional problem is ensured.Numerical results are presented.

Stefan UlbrichTechnische Universitaet DarmstadtFachbereich Mathematikulbrich@mathematik.tu-darmstadt.de

Jan Carsten ZiemsTU Darmstadtziems@mathematik.tu-darmstadt.de

MS73

Coupling Molecular and Continuum Modeling forDetailed Reaction Kinetics of TRISO Fuel Coating

Chemical vapor deposition of silicon carbide is applied inTRISO coatings for uranium kernels used as nuclear fuelin high-temperature gas-cooled reactors. The gas-phase re-action mechanisms will be determined using ab initio elec-tronic structure theory to provide initial parameters neededto predict rate constants, namely activation energies andstructural features, to calculate the appropriate partitionfunctions. The detailed chemical kinetics will be used as in-put into simulations using a continuum-based code, MFIX.

Francine BattagliaIowa State UniversityMechanical Engineeringfrancine@iastate.edu

Rodney O. FoxIowa State UniversityChemical and Biological Engineeringrofox@iastate.edu

Mark S. Gordon, Yingbin GeIowa State UniversityChemistrymark@si.fi.ameslab.gov, yingbin@si.fi.ameslab.gov

MS73

Quadrature-Based Moment Methods for Polydis-perse Multiphase Flows

The fundamental description of gas-solid flows begins witha kinetic equation for the particle-velocity distributionfunction. In the Eulerian representation of gas-solid flow,the moments of the kinetic equation are used to describethe particle density, the mean velocity, and selected sec-ond moments of velocity. However, the transport equa-tions for these moments are not closed due to (at least)two terms: (i) spatial transport by the fluctuating veloc-ity, and (ii) particle-particle interactions (e.g. collisions).In addition, systems with a distribution of particle prop-erties (i.e., polydisperse systems) lead to a kinetic equa-tion of higher dimensionality, and moment transport equa-tions with even more unclosed terms. In this talk we willdemonstrate how quadrature methods applied to the ki-netic equation can be used to derive consistent closures forthe moment equations. In particular, we will show thateven the simplest case of non-interacting particles with fi-nite Stokes number can be treated correctly using a quadra-ture approach, whereas “standard” multi-fluid models fail.We also show that the Boltzmann collision kernel can besuccesfully treated using quadrature to capture nonequi-librium flows.

Rodney O. FoxIowa State UniversityDepartment of Chemical & Biological Engr.rofox@iastate.edu

Prakash VedulaUniversity of Oklahomapvedula@ou.edu

MS73

Wavelet-Based Multiscale Approach for Heteroge-neous Chemically Reactive Flows: A Simple CaseStudy of Diffusion/Reaction Problem

This talk will give an overview of a general wavelet-basedmultiscale methodology called Compound Wavelet Matrix(CWM) and how it can be used to bridge spatial and tem-poral scales. In particular, the effectiveness of this methodin bridging scales in a simple reaction/diffusion problemwill be presented as an illustration of the CWM strategyfor multiscale/multiphysics models. In conclusion, the nextsteps needed to generalize the current methodology for ar-bitrary heterogeneous chemically reacting flows will be pre-sented.

Stuart DawOak Ridge National Laboratorydawcs@ornl.gov

Rodney O. FoxIowa State UniversityDepartment of Chemical & Biological Engr.rofox@iastate.edu

Sudib MisraUniversity of Arizonasudib@email.arizona.edu

Phani NukalaOak Ridge National Laboratorynukalap@ornl.gov

CS07 Abstracts 135

Pierre DeymierUniversity of Arizonadeymier@u.arizona.edu

Sreekanth PannalaComputer Science and Mathematics DivisionOak Ridge National Laboratorypannalas@ornl.gov

Srdjan SimunovicComputer Science and MathematiOak Ridge National Laboratorysimunovics@ornl.gov

Geroge FrantziskonisUniversity of Arizonafrantzis@email.arizona.edu

MS73

Multiscale/Multiphysics Methods Used in Hetero-geneous Chemically Reacting Flows

This talk will provide an overview of modeling multiphasechemical reactors and the various methods currently usedwhich span ¿10 orders of magnitude in both temporal andspatial scales. This includes a wide-variety of models likeDFT, Lattice Boltzmann methods, Discrete particle simu-lations, CFD and process models. This presentation willalso address the obstacles that need to be addressed to im-prove the integration across the scales and predictability ofthe overall device scale simulations.

Thomas O’BrienNational Energy Technology LaboratoryMorgantown, WVTHOMAS.OBRIEN@netl.doe.gov

MS74

A Bridging Domain Method for Coupling Continuawith Molecular Dynamics

A bridging domain method for coupling continuum mod-els with molecular models is described. In this method,the continuum and molecular domains are overlapped ina bridging subdomain, where the Hamiltonian is taken tobe a linear combination of the continuum and molecularHamiltonians. We enforce the compatibility in the bridg-ing domain by Lagrange multipliers or by the augmentedLagrangian method. An explicit algorithm for dynamicsolutions is developed. Results show that this multiscalemethod can avoid spurious wave reflections at the molec-ular/continuum interface without any additional filteringprocedures, even for problems with significant nonlinearit-ics. The method is also shown to naturally handle the cou-pling of the continuum energy equation with the molecularsubdomain. A multiple-time-step algorithm is also devel-oped within this framework.

Shaoping XiaoMechanical and Industrial EngineeringUniversity of Iowashaoping-xiao@uiowa.edu

Ted BelytschkoNorthwestern UniversityDept. of Mechanical Engineeringtedbelytschko@northwestern.edu

MS74

Generalized Mathematical Homogenization ofAtomistic Media at Finite Temperatures in ThreeDimensions

We derive thermo-mechanical continuum equations fromMolecular Dynamics (MD) equations using the General-ized Mathematical Homogenization (GMH) theory devel-oped by the authors for 0K applications. GMH constructsan array of atomistic unit cell problems coupled witha thermo-mechanical continuum problem. The unit cellproblem derived is a molecular dynamics problem definedfor the perturbation from the average atomistic displace-ments subjected to the deformation gradient and temper-ature extracted from the continuum problem. The coarsescale problem derived is a constitutive law-free continuumthermo-mechanical equation. Attention is restricted toheat transfer by lattice vibration (phonons). The methodis verified on several model problems against the referencemolecular dynamics solution.

Jacob FishDepartment of Mechanical, Aerospace & NuclearEngineeringRensselaer Polytechnic Institutefishj@rpi.edu

MS74

Phonon Heat Bath Approach for the Atomistic andMultiscale

A novel approach to modeling the crystalline solid as a heatbath is proposed. The approach is reducing the physicaldomain to an MD-solvable size. Interface with the hypo-thetic exterior region is non-reflective for outward elasticwaves, and provides adequate statistical correlation for theatomic thermal vibration by utilizing Gibbs canonical dis-tribution for the phonon gas in thermodynamic equilibriumat constant temperature. All method parameters are de-rived from the interatomic potential. Benchmark applica-tions are shown.

Eduard KarpovMECHANICAL, AEROSPACE, & BIOMEDICALENGINEERINGUniversity of Tennesseeedkarpov@gmail.com

MS74

Perfectly Matched Multiscale Simulations

A multiscale method is proposed. It combines the so-calledbridging scale method and the perfectly matched layermethod to form a robust and versatile multiscale algorithm.The method can efficiently eliminate the spurious reflec-tions/diffractions from the artificial atomistic/continuuminterface by matching the impedance at the interface ofthe molecular dynamic region and the perfectly matchedlayer. Moreover, it is shown in this paper that the methodcan capture anharmonic interaction among nonuniformlydistributed atoms in a local region.

Shaofan LiDepartment of Civil and Environmental Engineering,University of California, Berkeley,li@ce.berkeley.edu

Albert ToMechanical Engineering

136 CS07 Abstracts

Northwestern Universitya-to@northwestern.edu

MS75

High-Resolution Central Schemes for Kinetic andFluid Plasmas Models

In this work we present high-reslution central schemes fortwo-species plasmas described by the microscopic Vlasovmodel and by the macroscopic Euler-Poisson fluid model.Finite volume schemes for both models have been recentlydeveloped so as to asess the validity of the fluid model bycomparing the results obtained to those obtained with itskinetic counterpart. We propose the development of fi-nite volume schemes based on central differencing. Centralschemes avoid the costly use of Riemann solvers for thefluid model, resulting in simple numerical schemes.

Jorge BalbasUniversity of MichiganDepartment of Mathematicsjbalbas@umich.edu

MS75

A Hybrid Particle/Continuum Simulation Methodfor Coulomb Collisions in a Plasma

For small Knudsen number, simulation of of particles dy-namics by Monte Carlo becomes computationally inten-sive. In the context of rarefied gas dynamics, we havedeveloped an accelerated, hybrid method that combinesDSMC and a continuum solver. The molecular distribu-tion function f is represented as a linear combination of aMaxwellian distribution M and a particle distribution g;i.e., f = bM + (1 − b)g. The density, velocity and temper-ature of M are governed by fluid-like equations, while theparticle distribution g is simulated by Monte Carlo. In ad-dition there are interaction terms between M and g. Thecoefficient b is determined automatically, by a thermaliza-tion approximation. This talk will describe an extensionof the hybrid method to Coulomb collisions in a plasma.For this extension, the underlying Monte Carlo method isNanbu’s method for Coulomb collisions.

Russel CaflischUniversity of California, Los Angelescaflisch@math.ucla.edu

MS75

Numerical Heating and Particle Codes

Plasmas (ionized gases) have rich and complex behaviorwhich often need multiple lines of attack to fully under-stand their rich dynamics. Depending on the length scalesinvolved, the plasma may be described by either a kineticor a fluid model, the kinetic model being the more funda-mental of the two. In this talk we will give a brief overviewof the relation between these two models and then discussLagrangian particle methods for kinetic plasma problems.In particular, we will discuss the issue of numerical heat-ing in a verity of grid-based and grid-free particle methods( time stepping errors, mesh based effects, particle shapefunctions and nonlinear coupling of statistical errors to longrange fields.)

Andrew J. ChristliebMichigan State UniverityDepartment of Mathematicschristlieb@math.msu.edu

MS75

An Unstaggered Constrained Transport Methodfor 3D Ideal MHD

The ideal magnetohydrodynamic (MHD) system is a fluidmodel for a perfectly conducting quasi-neutral plasma.One of the main challenges in numerically solving theseequations is the requirement from Maxwell’s equations thatthe magnetic field remain divergence-free for all time (nomagnetic monopoles). The continuous equations automati-cally preserve this relationship, but standard numerical dis-cretizations do not. Furthermore, in many numerical com-putations, the failure to satisfy a discrete divergence-freeconstraint leads to (sometimes violent) numerical instabil-ities. In this talk we will review the constrained transportframework of Evans and Hawley [Astrophysical Journal,1988] and describe a new version of their approach thatis spatially unstaggered and relies on a magnetic potentialto maintain discrete divergence-free magnetic fields. A keyingredient in this approach is a new flux limiting strategythat maintains essentially non-oscillatory magnetic fieldsindirectly through the use of limiters on the magnetic po-tential equations. Several 2D and 3D simulations will bepresented to show the merit of the proposed method.

James A. RossmanithUniversity of WisconsinDepartment of Mathematicsrossmani@math.wisc.edu

MS76

Low-Rank Tensor Product Approximations forStochastic PDEs

One way to quantify uncertainty is via stochastic models,resulting often in a stochastic PDE (SPDE). Galerkin dis-cretisations of such linear and non-linear SPDEs result inhuge and complex systems of linear or non-linear equations.As the information amount in such a stochastic/physicaldiscretisation can be enormous, it is important to havesome way of compressing it. Low-rank tensor-product ap-proximations are one possibility for this, and their use isdescribed in this context.

Hermann G. MatthiesInstitute of Scientific ComputingTechnical University BraunschweigH.Matthies@tu-bs.de

MS76

Stochastic Collocation and Stochastic Galerkin forTime Dependent SPDEs

We study numerical approximations for the statistical mo-ments of the solution of a time dependent PDE, illustrat-ing on the computation of the expected value and deriv-ing a priori estimates of the resulting numerical errors.We apply a non-intrusive Stochastic Collocation Methodwhich is very versatile. It entails solving a number of stan-dard deterministic PDEs, precisely like in the Monte Carlomethod. We will discuss implementation issues and presentnumerical examples.

Fabio NobileMOX, Dip. di MatematicaPolitecnico di Milanofabio.nobile@polimi.it

Raul Tempone

CS07 Abstracts 137

School of Computational Science and MathematicsDepartmentFlorida State Universityrtempone@scs.fsu.edu

MS76

Sparse Second Moment Analysis of Elliptic Prob-lems in Stochastic Domains

We consider the numerical solution of elliptic problemsin domains with a class random boundary perturbations.Assuming perturbations with small amplitude and knownmean field and two-point correlation function, we derive,using a second order shape calculus, deterministic equa-tions for the mean field and the two-point correlation func-tion of the random solution in the stochastic domain. Us-ing a variational boundary integral equation formulationon the unperturbed, ‘mean’ boundary and a wavelet dis-cretization, we present and analyze an algorithm to approx-imate the random solution’s two-point correlation functionat essentially optimal order in essentially O(N ) work andmemory, where N denotes the number of unknowns re-quired for consistent discretization of the boundary of thedomain. Joint work w. Reinhold Schneider (Kiel) and Hel-mut Harbrecht (Bonn).

Christoph SchwabETH ZuerichSAMchristoph.schwab@sam.math.ethz.ch

MS76

Spectral Methods for Random Differential Equa-tions

This talk focuses efficient spectral methods for PDEs withrandom inputs. Spectral expansions based on the general-ized polynomial chaos (gPC) are employed in random spaceto approximate the random quantities. Stochastic Galerkinor stochastic collocation method is then employed to con-vert the stochastic PDEs into a set of deterministic PDEs,which can be solved via standard methods. Examples forpractical applications are presented.

Dongbin XiuDepartment of MathematicsPurdue Universitydxiu@math.purdue.edu

MS77

OOF: Analyzing Material Microstructure

The OOF program, developed at NIST, analyzes the prop-erties of materials with complicated microstructures. OOFallows a user to assign various material properties to thefeatures in a real or simulated microstructure, and usesfinite element analysis to predict the behavior of the mi-crostructure in virtual experiments. I will present the cur-rent version of the program, OOF2, and discuss featuresof its structure designed to make it easy to integrate withcomputations on different scales.

Stephen LangerInformation Technology LaboratoryNational Institute of Standards and Technologystephen.langer@nist.gov

MS77

RheoPlast: Open-Source Modular Parallel FiniteDifference Phase Field Software

RheoPlast is a multi-physics finite difference simula-tion code which includes modules for: binary andternary Cahn-Hilliard and vector-valued Allen-Cahn phasefield, transport-limited electrochemistry, velocity-vorticityand velocity-pressure flow, elastic shear strain for fluid-structure interactions, and heat conduction; these can becombined arbitrarily at runtime. Based on the PETScsuite of parallel solvers and data objects, RheoPlast runsin two or three dimensions, features flexible time stepping,and can use periodic, symmetry, and module-specific pro-grammed boundary conditions.

Adam C. PowellVeryst Engineering LLCapowell@veryst.com

MS77

Computational Informatics for Materials Design

In this presentation we discuss how statistical learningtechniques can be used to augment more classical ap-proaches to computational based design of materials. Therole of data mining to identify dominant parameters influ-encing phase stability calculations is demonstrated. Theuse of such informatics based techniques to accelerate thecomputational approaches for first principle calculations isdiscussed. Examples are provided for a variety of multi-component alloy design platforms.

Krishna RajanDepartment of Materials Science and EngineeringIowa State Universitykrajan@iastate.edu

MS77

On-Line Microstructure Repository for PredictiveAnalyses

Many materials properties can be understood by analyz-ing the temporal and spatial evolution of microstructuresunder different conditions. Performing such analysis re-quires compact representation to store and manipulate alarge set of microstructures and techniques to determinerelationships between properties, structure and processingparameters from such large data sets. We discuss how thesechallenges can be addressed through computational andsoftware techniques implemented in our web-portal appli-cations for designing Aluminum-rich alloys.

Zi-Kui LiuDepartment of Materials Science and EngineeringPenn State Universityzikui@matse.psu.edu

Keita TeranishiDepartment of Computer Science and EngineeringThe Pennsylvania State Universityteranish@cse.psu.edu

Padma RaghavanThe Pennsylvania State Univ.Dept of Computer Science Engr.raghavan@cse.psu.edu

Long-Qing Chen

138 CS07 Abstracts

Materials Science and EngineeringPenn State Universitychen@ems.psu.edu

MS78

Simulation of Supersonic Combustion Phenomenain Evolving Geometries with Cartesian UpwindMethods

Accurate numerical simulation of gaseous high-speed com-bustion in evolving domains requires the integrated appli-cation of several advanced techniques: consideration of stiffchemical kinetics, parallelization, and (in our case) em-bedding of moving boundaries into a dynamically adaptiveCartesian mesh. The core component though is a reliablehigh-resolution upwind scheme for gas-mixtures with com-plex equation of state. The presentation compares wave-propagation-based methods with standard shock-capturingschemes and evaluates suitability and performance for sim-ple and practically relevant configurations.

Ralf DeiterdingOak Ridge National Laboratorydeiterdingr@ornl.gov

MS78

High-Resolution Finite Volume Methods for a Bi-ological Problem

Extracorporeal Shock Wave Therapy is a noninvasive tech-nique for the treatment of a variety of musculoskeletal con-ditions such as bone fractures and plantar fasciitis. Inlithotripsy, a shock wave is generated in a liquid bath, fo-cused by an ellipsoidal reflector, and it then propagatesinto the body where it strikes the treatment area. We usehigh-resolution finite volume methods to solve the nonlin-ear elasticity equations and model the shock wave propa-gation in bone and tissue.

Randall J. LeVequeApplied MathematicsUniversity of Washington (Seattle)rjl@amath.washington.edu

Kirsten FagnanUniversity of Washingtonkfagnan@amath.washington.edu

MS78

Numerical Simulations of a Multi-Scale Model forSuspensions of Rod-like Molecules

We consider the Doi model for suspensions of rigid rod-like molecules. The model couples a microscopic Fokker-Planck type equation (the Smoluchowski equation) to amacroscopic Stokes equation. The Smoluchowski equationdescribes the evolution of the distribution of the rod orien-tation. It is a drift-diffusion equation on the sphere whichis solved in every point of the macroscopic flow domain.The coupled flow problem shows interesting behavior, inparticular the spurt phenomenon. In the spurt regime, thedrift term in the Smoluchowski equation is dominant andthus a discretization based on the wave propagation algo-rithm is used to approximate the coupled micro-macro flowproblem.

Christiane HelzelUniversity of Bonn

Department of Applied Mathematicshelzel@iam.uni-bonn.de

MS78

Finite Volume Modeling of Acoustic and ElasticWaves in Periodic Media

I will briefly present the basic ideas of WENOCLAW,a high order accurate finite volume method built withinthe CLAWPACK framework. WENOCLAW combines theideas of wave propagation and high order WENO recon-struction. I will then discuss the application of WENO-CLAW to acoustics and elastics in heterogeneous media.The wave propagation algorithm easily handles the numer-ical difficulties associated with discontinuous material pa-rameters, while the WENO reconstruction yields high or-der accuracy. I will show results of calculations of bandgapsin sonic crystals, focusing via acoustic lenses, and solitarywaves in periodic two-dimensional elastic media.

David I. KetchesonUniversity of WashingtonDept. of Applied Mathematicsdketch@gmail.com

MS79

A Posteriori Error Estimation For DiscontinuousGalerkin Methods

Discontinuous Galerkin methods (DGM) have gained inpopularity during the last 30 years because of their abilityto address problems having discontinuities, such as thosethat arise in hyperbolic conservation laws. The DGM use adiscontinuous finite element basis which simplifies hp adap-tivity and leads to a simple communication pattern acrossfaces that makes them useful for parallel computation. Inorder for the DGM to be useful in an adaptive setting, tech-niques for estimating the discretization errors should beavailable both to guide adaptive enrichment and to providea stopping criteria for the solution process. We will presentnew superconvergence results on triangular elements andshow how to construct effective estimates of the finite el-ement discretization error using superconvergence of DGsolutions. First, we present new O(hp+2) pointwise super-convergence results for first-order hyperbolic problems ontriangular meshes consisting of one-outflow-edge elementsas well as on meshes having both one- and two-outflow-edgeelements. We will present efficient techniques to computeasymptotically correct a posteriori error estimates obtainedby solving local problems.

Slimane AdjeridDepartment of MathematicsVirginia Polytechnic Institute and State Universityadjerids@vt.edu

Mahboub BaccouchDepartment of MathematicsVirginia Polytechnic Institute and State Universitybaccouch@math.vt.edu

MS79

A Posteriori Error Estimates, Error Control, andModel Sensitivity

Investigating and exploiting the sensitivity of a model withrespect to data and parameters is a fundamental problemin CS&E. This involves computing solutions correspond-

CS07 Abstracts 139

ing to different data and parameter values, and thereforehaving different properties. This raises a critical need forerror estimation and control since otherwise numerical er-ror can mask the true responses. In this talk, we developthe computational aspects of dealing with model sensitivityby means of a posteriori error analysis.

Donald EstepColorado State Universityestep@math.colostate.edu

David NeckelsSandia National Laboratoriesdcnecke@sandia.gov

Victor Ginting, Sheldon LeeDepartment of MathematicsColorado State Universityginting@math.colostate.edu, lee@math.colostate.edu

Rebecca MckeownNatural Resource Ecology LaboratoryColorado State Universitybeckym@nrel.colostate.edu

Jeff SandelinDepartment of MathematicsColorado State Universityjtsandelin@comcast.net

MS79

A Posteriori Error Estimates for Eigenvalue Anal-ysis of Heterogeneous Elastic Structures

For eigenvalue analysis of heterogeneous elastic structures,a posteriori error estimators are less studied than the es-timators for traditional static elliptic or time-dependentproblems. In this talk, we will present an explicit esti-mator that treats the cases of high order finite elementsand discontinuous material coefficients. This estimator isequivalent with the error in the eigenvector, independentlyof the variation of the materials properties. We will assessthe efficiency of this estimator with numerical experiments.

Garth ReeseSandia National Laboratoriesgmreese@sandia.gov

Tim WalshSandia National Labstfwalsh@sandia.gov

Ulrich L. HetmaniukSandia National Laboratoriesulhetma@sandia.gov

MS79

Adaptive Simulation of Multiphysics Problems

In this talk we outline a basic framework for adaptive sim-ulation of multiphysics problems. The adaptive algorithmsare based on a posteriori error estimates that account forthe overall effect on output goal quantities of the errorscaused in the individual single physics solvers and in thetransfer of data between these solvers. The framework isillustrated on several applications including multiphysicssimulation of oil reservoirs, mems devices, and electronics

cooling.

Mats LarsonDepartment of MathematicsUmea Universitymats.larson@math.umu.se

MS80

Overlapping Grids for Interface and MovingBoundary Problems

The overlapping grid approach can be used to accuratelytreat problems with interfaces and moving boundaries. Ina typical grid construction, narrow boundary fitted gridsare used to represent the moving boundary or interface,and these grids overlap with stationary background Carte-sian grids. In this talk I will discuss several examples ofusing overlapping grids to handle problems with interfacesand moving boundaries including results for the reactive-Euler equations, incompressible fluid flow and Maxwell’sequations.

William D. HenshawCASCLawrence Livermore National Labhenshaw@llnl.gov

MS80

Front Tracking Simulation of Shock Bubble Inter-action

In this presentation, we study shock-bubble multiple in-teractions through reflecting boundaries using the fronttracking method. We make a systematic exploration ofthe single shock passage problem in a range of dimension-less parameters. We then extend our computational studyto multiple re-shocks produced by reflecting boundaries.We use fast Fourier transform (FFT) to analyze the spec-tra of kinetic energy and vorticity and compare with thenon-tracking simulations.

Xiaolin LiDepartment of Applied Math and StatSUNY at Stony Brooklinli@ams.sunysb.edu

MS80

The Moving Contact Line Problem

The moving contact line problem is a classical problem influid mechanics. The difficulty stems from the fact thatthe classical continuum theory with no-slip boundary con-dition predicts a non-physical singularity at the contactline with infinite rate of energy dissipation. Many modi-fied continuum models are then proposed to overcome thisdifficulty. They all succeed in removing the singularity,but they leave behind the question: which one of thesemodels is a good description of the microscopic physicsnear the contact line region? We will review the resultsobtained using continuum theory, molecular dynamics andthe more recent multiscale techniques. We will also discusshow these techniques can be combined to give us a betterunderstanding of the fundamental physics of the movingcontact line and formulate simple and effective models

Weiqing RenCourant Institute of Mathamatical SciencesNew York Universityweiqing@cims.nyu.edu

140 CS07 Abstracts

MS80

A High-Resolution Godunov Method for Reactiveand Nonreactive Multi-Material Flow on Overlap-ping Grids

A numerical method is described for reactive and nonreac-tive multi-material flow. The flow is governed by the multi-material reactive Euler equations with a general mixtureequation of state. Composite overlapping grids are used tohandle complex flow geometry and block-structured adap-tive mesh refinement (AMR) is used to locally increasegrid resolution near shocks, material interfaces and reac-tion zones. The discretization is based on a high-resolutionGodunov method, but includes an energy correction de-signed to suppress numerical errors that develop near a ma-terial interface for standard, conservative shock-capturingschemes. Nonreactive flow involving shock interactionswith planar and curved inhomogeneities and reactive flowinvolving detonation diffraction are discussed to illustratethe numerical approach.

Jeffrey BanksSandia National Laboratoryjwbanks@sandia.gov

Donald W. SchwendemanRensselaer Polytechnic Instituteschwed@rpi.edu

MS81

Theory and Discretization of Operator RiccatiEquations

In this paper we focus on the problem of developing numer-ical schemes that yield convergent and mesh independentapproximations of the infinite dimensional Riccati equation

F(X ) = A∗X + XA− XBB∗X + C∗C = ′,

where BB∗, CC∗ ∈ L(H) and A generates a stronglycontinuous semigroup on a Hilbert space H. We con-sider a sequence of approximating problems defined by(HN , AN , BN , CN ), where HN ⊂ H is a sequence offinite dimensional subspaces of H, AN ∈ L(HN ,HN ),BN ∈ L(U ,HN ) and CN ∈ L(HN ,Y) are bounded lin-ear operators. Let PN : H → HN denote the orthogonalprojection of H onto HN satisfying

∥∥PN∥∥ ≤ 1 and assume

that ‖PNx − Px‖ → 0 as N → ∞ for all x ∈ H. Definethe finite dimensional approximating Riccati equations by

FN (XN ) = (AN )∗X+XAN−XNBN (BN )∗XN+(CN )∗CN = ′.

Let Xk ∈ L(H) denote the iterates of the Newton methodfor the infinite dimensional Riccati equation F(X ) = ′.Likewise, XN

k ∈ L(HN ) denotes the iterates of the Newtonmethod for the discretized Riccati equation FN (XN ) = ′.Roughly speaking, the MIP may be broken down intoconvergence under mesh refinement and Newton intera-tion counts on a given mesh. We first review the con-ditions on the approximating scheme (HN , AN , BN , CN )which are sufficient to imply that the approximating Ric-cati equation admits a unique nonnegative solution XN

∞,and XN

∞PN converges to the unique nonnegative solutionX∞ of the infinite dimensional operator Riccati equation.We then focus on the issue of mesh independence for theKleinman-Newton algorithm. In particular, we present re-sults that relate mesh independence to dual convergenceand the preservation of control system properties under

approximation. Finally, we provide applications and nu-merical examples to illustrate the ideas.

John BurnsInterdisciplinary Center for Applied MathematicsVirginia Techburns@silver.icam.vt.edu

MS81

A Comparsion of Multigrid and H-ADI for LargeScale Riccati Equations

We compare two related multilevel methods for the so-lution of large scale algebraic matrix Riccati equationsAX + XAT − XFX + C = 0: A (nonlinear) multigridmethod and an ADI iteration based on hierarchical matri-ces. Both approaches can be adapted in order to preservethe low rank structure of the n× n solution X induced bylow rank right-hand sides C, so the equation can be solvedin almost linear complexity O(n logc n).

Lars GrasedyckMax-Planck-InstituteMath in Scienceslgr@mis.mpg.de

MS81

Iterative Solution of ARE’s Arising in Control ofVibrations

Algebraic Riccati equations (ARE) of large dimension arisewhen using approximations to design controllers for sys-tems modelled by partial differential equations. A numberof approaches to solving such algebraic Riccati equationsexist. Most rely on finding a low rank approximation tothe exact solution. For some problems, such as heatingproblems, this low rank approximation exists. Numericalresults indicate that for weakly damped problems a lowrank solution to the ARE may not exist. Further analysissupports this point.

Kirsten MorrisDept. of Applied MathematicsUniversity of Waterlookmorris@uwaterloo.ca

MS81

Low Rank Approximate Solution of Algebraic Ric-cati Equations

A method is developed for the approximate low rank solu-tion of several important problems in control, including thesolution of large scale algebraic Riccati equations as theyarise in optimal control, H-infinity control and in modelreduction. The solutions are obtained through the approx-imate computation of a basis for a selected invariant sub-space of a block structured matrix pencil. The subspacebasis is used to construct low rank approximate solutions toRiccati equations, in particular to the maximal and mini-mal symmetric solutions. This approach yields approxima-tion results that guarantee stability and passivity in modelreduction of passive systems.

Volker MehrmannTechnische Universitat Berlinmehrmann@math.tu-berlin.de

Peter BennerU. Chemnitz

CS07 Abstracts 141

benner@mathematik.tu-chemnitz.de

Danny C. SorensenRice Universitysorensen@rice.edu

MS82

Adaptive Refinement for the Solution of Maxwell’sEquations

Abstract not available at time of publication.

Eldad HaberEmory UniversityDept of Math and CShaber@mathcs.emory.edu

MS82

Talk Title Not Available at Time of Publication

Abstract not available at time of publication.

Gregory NewmanLBLGANewman@lbl.gov

MS82

Discontinuous Galerkin Methods for the Time-Harmonic Maxwell Equations

We propose and analyze interior penalty discontinuousGalerkin methods for the numerical discretization of thetime-harmonic Maxwell equations. The main advantagesof these methods in comparison with conforming finite el-ement approaches lie in their high flexibility in the mesh-design and their accommodation of high-order elements.We derive the methods for the time-harmonic Maxwellequations, and discuss the underlying stability mecha-nisms. Based on suitable duality arguments, we then deriveoptimal a-priori error bounds in the energy norm and theL2-norm. Finally, we present a-posteriori error estimatorsfor the low-frequency approximation of the time-harmonicMaxwell equations where the resulting bilinear forms arecoercive. We show the reliability and efficiency of the es-timators and demonstrate numerically that they can effi-ciently resolve the strongest Maxwell singularites in non-smooth domains. We derive the methods for the incom-pressible Navier-Stokes equations, and discuss the under-lying stability mechanisms. We then develop the a-prioriand a-posteriori error estimation of hp-adaptive discretiza-tions and present adaptive refinement procedures. All ourtheoretical results are illustrated and verified in numericalexperiments.

Dominik SchoetzauMathematics DepartmentUniversity of British Columbiaschoetzau@math.ubc.ca

MS82

Algebraic Multigrid and Algebraic Reformulationsof the Eddy Current Equations

With the rising popularity of compatible discretizations(edge elements) for the eddy current Maxwell’s equations,there is a corresponding need for fast solvers. We proposean algebraic reformulation of the discrete system alongwith a new AMG technique for this reformulated prob-

lem. This technique requires a specialized solver on the finemesh, but traditional methods can be used on the coarsermeshes. We illustrate the new technique for smoothed ag-gregation AMG and present computational results.

Pavel Bochev, Christopher SiefertSandia National Laboratoriespbochev@sandia.gov, csiefer@sandia.gov

Ray S. TuminaroSandia National LaboratoriesComputational Mathematics and Algorithmsrstumin@sandia.gov

Jonathan J. HuSandia National LaboratoriesLivermore, CA 94551jhu@sandia.gov

MS83

BGCE - The Bavarian Graduate School of Compu-tational Engineering

The Bavarian Graduate School of Computational En-gineering (BGCE) was established as kind of an um-brella programme, gathering three CSE-related graduateprogrammes at TU Munich and University of Erlangen-Nuremberg. For the best students there, BGCE offers anelite track which, after successful participation, leads to amaster’s degree with honours. The talk will present theBGCE as the funding institution of this student prize.

Hans BungartzTU-Muenchenbungartz@in.tum.de

MS83

Title Not Available at Time of Publication

Abstract not available at time of publication.

Ulrich J. RuedeUniversity of Erlangen-NurembergDepartment of Computer Science (Simulation)ruede@cs.fau.de

MS84

Title Not Available at Time of Publication

Abstract not available at time of publication.

Derek BinghamDept. of Statistics and Actuarial ScienceSimon Fraser Universitydbingham@cs.sfu.ca

MS84

Treed Gaussian Processes for Surrogate ModelingUnder Uncertainty

One important contribution of statistics is in the develop-ment of surrogate models which can give a computationallyfast approximate response surface for a function, such asthe output of complex computer code. The traditional ap-proach to surrogate modeling uses Gaussian process mod-els, but they have a number of potential problems. Wepresent a more flexible model, based on a treed partitionof the space, with Gaussian processes fit within each parti-

142 CS07 Abstracts

tion. By doing so in a fully Bayesian manner, we can alsogive complete uncertainty estimates, which can then beused for guiding searches of the input space for either op-timization or learning about the unknown function itself.We demonstrate this approach on our motivating exam-ple of the adaptive design of a simulation experiment forlearning the response surface of flight characteristics of aproposed rocket booster.

Herbie LeeUniversity of California, Santa CruzDept. of Applied Math & Statisticsherbie@ams.ucsc.edu

MS84

Title Not Available at Time of Publication

Abstract not available at time of publication.

Monica Martinez-CanalesComputational Sciences and Mathematics ResearchDepartmentSandia National Laboratories, Livermore, CA.mmarti7@sandia.gov

MS84

Pattern Search Optimization with a Treed Gaus-sian Process Oracle

The derivative-free optimization method AsynchronousParallel Pattern Search (APPS) allows use of an external’oracle’ to help guide the optimization search. Here weincorporate statistical modeling via Treed Gaussian Pro-cesses as the oracle. Using a statistical model allows us toexplicitly quantify our uncertainty about the function out-put, leading to a more robust global optimization. We alsoinvestigate the use of statistical inference in convergencecriteria, so as to include globally informed stopping rules.

Matt TaddyUniversity of California, Santa CruzDept of Applied Math & Statisticstaddy@soe.ucsc.edu

MS85

The Cactus Framework: Design, Applications andFuture Directions

The Cactus Code is an opensource, modular frameworkfor collaborative high-performance computing. In additionto including different computational and community toolk-its, Cactus provides a range of abstract interfaces to appli-cation developers through which a variety of third partylibraries and tools can be easily leveraged. In this talk,we review the design of Cactus, describe how it is usedby different application communities, and discuss ongoingdevelopment plans for supporting new application needs.

Gabrielle AllenCenter for Computation & TechnologyLouisiana State University, Baton Rouge, LA 70803gallen@cct.lsu.edu

MS85

AMROC - A Cartesian SAMR Framework forCompressible Gas Dynamics

AMROC is an object-oriented C++ framework that pro-

vides structured adaptive mesh refinement (SAMR) on dis-tributed memory machines. Being the fluid solver systemof Caltech’s simulation infrastructure ”Virtual Test Facil-ity”, the current main applications range from Eulerian-Lagrangian fluid-structure interaction simulation to su-personic combustion and turbulence modeling in complex(evolving) geometries. The presentation details the de-sign and generic components that enable the constructionof large-scale parallel simulation codes involving Euleriancompressible gas dynamics in minimal time.

Ralf DeiterdingOak Ridge National Laboratorydeiterdingr@ornl.gov

MS85

Integrating Modeling and Simulation Componentswithin the SIERRA Framework

The SIERRA Framework provides modeling and simu-lation application codes with a collection of capabilitiesfor parallel execution, distributed adaptive unstructuredmeshes, and multiphysics coupling. Application codes in-tegrate their physics-specific components into the frame-work such that these components may be completely in-sulated from details of parallel communication and dis-tributed data synchronization. The SIERRA Frameworksparallel execution model, distributed mesh model, appli-cation components and taxonomy, and framework interac-tions with application components will be presented.

H. Carter EdwardsSandia National Laboratorieshcedwar@sandia.gov

MS85

Components for Adaptive Multiscale Simulations

This presentation will discuss a set of functional compo-nents being developed to support the execution of adap-tive multiscale simulations. The components are designedto accept a general specification of multiscale problems andto coordination the interactions of the simulation domainsand fields accounting for the transformations associatedwith going across the multiple scales in which various dis-cretization processes are used within each scale. Exam-ple adaptive applications including continuum to atomisticcoupling will be presented.

Mark S. ShephardRensselaer Polytechnic InstituteScientific Computation Research Centershephard@scorec.rpi.edu

MS86

The L2 Norm Error Estimates for the Div Least-Squares Method

This talk presents L2 norm error estimates for the div least-squares method for which the associated homogeneousleast-squares functional is equivalent to the H(div) × H1

norm for the respective dual and primal variables. Opti-mal L2 norm error estimates for the primal variable underthe minimum regularity requirement for the second-orderelliptic equations, elasticity, and the Stokes equations areestablished.

Z. CaiDepartment of mathematics

CS07 Abstracts 143

Purdue Universityzcai@math.purdue.edu

JaEun KuPurdue Universityjku@math.purdue.edu

MS86

Least-Squares Methods for Interface and Mesh Ty-ing Problems

In the finite element method, a standard approach to meshtying is to apply Lagrange multipliers. However, if the ad-joining surfaces do not coincide spatially, straightforwardLagrange multiplier methods lead to discrete formulationsfailing a first-order patch test. A least-squares method ispresented here for mesh tying in the presence of gaps andoverlaps. The least-squares formulation for transmissionproblems is extended to settings where subdomain bound-aries are not spatially coincident. The new method is con-sistent in the sense that it recovers exactly global polyno-mial solutions that are in the finite element space. As aresult, the least-squares mesh tying method passes a patchtest of the order of the finite element space by construc-tion. This attractive computational property is illustratedby numerical experiments.

Pavel BochevSandia National LaboratoriesComputational Math and Algorithmspbboche@sandia.gov

David DaySandia National Laboratoriesdmday@sandia.gov

MS86

First-Order System Least Squares FEM Approachfor Solving Maxwells Equations in Deforming Me-dia

Deformation of solid media brings the matter flow fieldand the Cauchy-Green and Piola strain tensors into theelectromagnetic constitutive laws, which renders Maxwell’sequations hyperbolic with variable coefficients. A numer-ical solution of the time-diecretized Maxwells equations isdeforming solid media based on a first-order system least-squares (FOSLS) variational formalism will be presented.

Anter El-AzabFlorida State UniversitySchool of Computational Science & MechanicalEngineering Depanter@eng.fsu.edu

MS86

First-Order System Ll* (fosll*) for Maxwell’s Equa-tions in 3D with Edge Singularities.

The L2–norm version of first–order system least squares(FOSLS) attempts to reformulate a given system of partialdifferential equations so that applying a least–squares prin-ciple yields a functional whose bilinear part is H1–elliptic.This means that the minimization process amounts to solv-ing a loosely coupled system of elliptic scalar equations. Anunfortunate limitation of the L2–norm FOSLS approach isthat this product H1 equivalence generally requires suffi-cient smoothness of the original problem. Inverse–norm

FOSLS overcomes this limitation, but at a substantial lossof real efficiency. The FOSLL* approach described hereis a promising alternative that is based on recasting theoriginal problem as a minimization principle involving theadjoint equations. This talk provides a theoretical foun-dation for the FOSLL* methodology and application tothe eddy current form of Maxwell’s equations. It is shownthat singularities due to discontinuous coefficients are eas-ily treated. However, singularities due to reentrant edgesrequire a further modification. A partially weighted normis used only on the slack equations. The solution retainsoptimal order accuracy and the resulting linear systems areeasily solved by multigrid methods. Comparison is madeto the curlcurl formulation and the weighted regularizationapproach. The FOSLL∗ is shown to have equal or betteraccuracy, obtained at a smaller cost. Numerical examplesare presented that support the theory.

Eunjung LeeUniversity of ColoradoDepartment of Applied Matheunjung.lee@colorado.edu

Thomas ManteuffelUniversity of Coloradotmanteuf@colorado.edu

MS87

Mathematical Modeling of Pollution Distributionfrom Motor Transport in City in Bottom Layer ofAtmosphere

In report there are 3D air-dynamics model in bottom layerof atmosphere and advection-diffusion model of transportpollution. Program realization of models based on GIStechnology and database for the pollution distribution incase of typical weather conditions. The first regime of pro-gram based on direct simulation gas dynamics, humidityand heat transport and finally air pollution distributionmodeling. The other variant based on fast searching ofmost similar variant for given situation from database.

Denis Lyubomishenko, Valery GadelshinTaganrog State University of Radio-Engineeringkolek007 @mail.ru, kolek007 @mail.ru

MS87

LBM Approaches for the Heat-Mass Transfer inShallow Water Basins

In recent years the lattice Boltzmann method (LBM) hasattracted much attention in the physics and engineeringcommunities as a possible alternative approach for solvingcomplex fluid dynamics problems. In particular, the inher-ent parallelism, the simplicity of programming, and the ca-pability of incorporating complex microscopic interactionshave made LBM a very attractive simulation method forfluid flow in complex physical systems, specifically in mod-eling of heat and mass transfer in shallow water basins.

Boris SidorenkoTaganrog State University of Radio-Engineeringsai@rec.tsure.ru

MS87

High Resolution Shallow Water Models and Its Ap-

144 CS07 Abstracts

plication to Some Basins in the South of Russia

In report 2D and 3D high precision models for shallow wa-ter basins have been presented. These models take intoaccount following factors: complicated form of beach andbottom, wind and bottom friction, Coriolis factor, inputand output, evaporation in mass conservation as well as inmomentum equations and so on. Also coefficients of tur-bulent diffusion have been computed. These models havebeen applied to the Azov Sea modeling and theoretical andexperimental results compared.

Alexander I. SukhinovTaganrog State University of Radio-Engineeringsukhinov@gmail.com

MS87

Modeling of Pollution Distribution in the Azov SeaUsing Irregular Grids

For numerical realization of high precision hydrodynamicmodel for shallow water basins the method of finite ele-ments on irregular triangular meshes is used. Unlike regu-lar meshes, irregular meshes are easier to build, they easilyadapt for complex geometry of area. It is developed origi-nal algorithms of irregular triangular meshes constructionbased on the mesh refining by moving nodes preservingDelaunay conditions fulfillment. Nodes also moved alongborders of the area in iterative process.

Anton SukhinovMoscow Institute of Physics and Technologysai@rec.tsure.ru

MS88

Challenges and Algorithms for Simulating AlfvenicTurbulence in Collisionless Plasma

Turbulence plays a critical role in plasma systems rang-ing from laboratory fusion experiments to astrophysics.In nearly collisionless systems, modeling this turbulence ischallenging because of the kinetic nature of the dominantdissipation processes and because of the strong nonlinearinteractions that control the dynamics. On the other hand,the range of spatio-temporal scales that must be simultane-ously resolved is not as large as in neutral fluid turbulence.A new class of ”gyrokinetic” codes developed for fusion arefacilitating the exploration of plasma turbulence across abroad range of problems. In astrophysics an important is-sue is how large-scale turbulent energy is absorbed as itcascades to small spatial scales. Whether the energy isdumped into electrons or ions in accretion flows and inother systems impacts both the dynamics of the systemand our ability to interpret observations through measure-ment of radiation from distant sites throughout the uni-verse. Results from the first self-consistent calculations ofthe collisionless absorption of turbulent energy cascades forastrophysical applications will be presented. A new mech-anism for ion heating in Alfvenic plasma turbulence willbe discussed, and a short discussion of the accuracy of thealgorithms used for this calculation will be presented.

Bill DorandUniversity of MarylandDepartment of Physicsbdorland@umd.edu

MS88

Discontinuous Galerkin Methods for Fluid Plasma

Modeling with Applications to Plasmoid Accelera-tors

Plasmoid accelerators are an interesting high energy den-sity propulsion concept currently under investigation atAdvatech Pacific in partnership with the Air Force Re-search Laboratory at Edwards Air Force Base. Approachesto fluid plasma modeling using the discontinuous Galerkinmethod are being developed to help better understandplasma physics issues important to this thruster concept.One promising approach involves the use of vector poten-tials to maintain the divergence constraint when time de-pendent magnetic field boundary conditions are applied.In this talk, discontinuous Galerkin algorithms for fluidplasma models will be presented along with numericalbenchmarks and results relevant to plasmoid propulsion.

Jean-Luc CambierAir Force Research LaboratoryPropulsion Directorate , AerophysicsJean-Luc.Cambier@edwards.af.mil

John J. LoverichAdvatech Pacific Inc.john.loverich@gmail.com

MS88

Advances in Mixed Materials Modeling for Resis-tive MHD on ALE Meshes

There is continued interest in the MHD modeling of mixedmaterials for a variety of high current plasma applications.The challenge is the constituents may be very small, requir-ing high spatial resolution. We show the protocol for using”microscopic” simulations, where the individual materialsare resolved, to build a ”macroscopic” EOS and resistiv-ity tables of a thermodynamically correct mixed, homoge-nized material at reduced resolution. Simulations will becompared against both microscopic calculations and exper-imental results.

John W. Luginsland, Michael Frese, Sherry FreseNumerExjohn.luginsland@numerex.com,michael.frese@numerex.com, sherry.frese@numerex.com

MS88

A Boltzmann-PIC-MCC Hybrid Model for Colli-sional Transport in the Tokamak Diverter Sheath

The plasma sheath and hydrocarbon transport near a car-bon diverter plate of a ITER-like tokamak is modeled usinga one-dimensional particle-fluid hybrid model, with a hy-brid Monte Carlo collision model. Electrons are modeledas an inertia-less (Boltzmann) fluid with conservation ofcharge enforced by a time-dependent flux balance at thewalls for a Maxwellian distribution at a specified temper-ature. Flux flows in from the edge plasma, and out at thediverter and also in the upstream direction. Ions are mod-eled using the PIC methodology. The modeling method-ology for the iterative nonlinear solver is presented. Thehybrid collision model allows particle-particle collisions aswell as particle-fuild and fluid-fluid collisions. The hybridmodel is shown to run about one hundred times faster thana full PIC model.

Christine NguyenUniversity of California - Berkeleyctine.nguyen@gmail.com

CS07 Abstracts 145

Chul Hyun Lim, Jeff HammelDept. Nuclear EngineeringUniversity of California - Berkeleychlim@langmuir.nuc.berkeley.edu, k0scist@gmail.com

John VerboncoeurDept. Nuclear EngineeringUniversity of Californiajohnv@nuc.berkeley.edu

MS89

Model Reduction and Adaptation in StochasticGalerkin Projections

This paper focuses on addressing issues of computationalefficiency of spectral stochastic Galerkin projections for thesolution of complex stochastic systems. In particular, analgorithm is developed for the efficient characterization ofa lower dimensional manifold occupied by the solution to astochastic partial differential equation (SPDE) in the Fockspace associated with the Wiener chaos. A description ofthe stochastic aspect of the problem on two well-separatedscales is developed to enable the stochastic characterizationon the fine scale using algebraic operations on the coarsescale. Moreover, a solid foundation is provided for theadaptive error control in stochastic Galerkin procedures.

Roger GhanemUniversity of Southern CaliforniaAerospace and Mechanical Engineering and CivilEngineeringghanem@usc.edu

Alireza DoostanUniversity of Southern CaliforniaAerospace and Mechanical Engineering and CivilEngineeringdoostan@jhu.edu

MS89

Uncertainty Quantification in ElectromagneticScattering

We shall discuss the use of polynomial chaos expansionsfor quantifing the impact of uncertainty in electromagneticscattering. Modeling of uncertainty in sources, materials,and geometries will be discussed and we will also compareGalerkin and Collocation forms of the polynomial chaosapproach. The EM problem is solved using a high-orderDG-FEM approach. We shall illustrate use of such tech-niques on problems of realistic complexity, including prob-lems requiring a high-dimensional random space.

Cedric ChauviereUniverity Blaise Pascal, Francecedric.chauviere@math.univ-bpclermont.fr

Laura LuratiIMA and Boeing, Seattlelaural@dam.brown.edu

Tim WarburtonRice Universitytim.warburton@gmail.com

Lucas WilcoxUniversity of Austin, Texaslucas.wilcox@gmail.com

Jan S. HesthavenBrown UniversityDivision of Applied MathematicJan.Hesthaven@Brown.edu

MS89

Stochastic Collocation Methods Nonlinear EllipticPDEs with Random Input Data

This work proposes and analyzes sparse grid stochasticcollocation techniques for solving nonlinear elliptic partialdifferential equations with random coefficients and forc-ing terms (input data of the model). This method canbe viewed as an extension of the Stochastic Collocationmethod proposed in [Babuska-Nobile-Tempone, Technicalreport, MOX, Dipartimento di Matematica, 2005] whichconsists of a Galerkin approximation in space and a col-location at the zeros of suitable tensor product orthogo-nal polynomials in probability space and naturally leads tothe solution of uncoupled deterministic problems as in theMonte Carlo method. The full tensor product spaces sufferfrom the curse of dimensionality since the dimension of theapproximating space grows exponentially fast in the num-ber of random variables. If the number of random variablesis moderately large, this work proposes the use of sparsetensor product spaces utilizing either Clenshaw-Curtis orGaussian interpolants. For both situations this work pro-vides rigorous convergence analysis of the fully discreteproblem and demonstrates: (sub)-exponential convergenceof the ”probability error” in the asymptotic regime andalgebraic convergence of the ”probability error” in the pre-asymptotic regime, with respect to the total number ofcollocation points. Numerical examples exemplify the the-oretical results and show the effectiveness of the method.

Fabio NobileMOX, Dip. di MatematicaPolitecnico di Milanofabio.nobile@polimi.it

Raul TemponeSchool of Computational Science and MathematicsDepartmentFlorida State Universityrtempone@scs.fsu.edu

Clayton G. WebsterFlorida State Universitywebster@scs.fsu.edu

MS89

Modeling Diffusion in Random Heterogeneous Me-dia: Data-Driven Microstructure ReconstructionModels, Stochastic Collocation and the VariationalMultiscale Method

We are interested in modeling diffusion in 3D random het-erogeneous microstructures that are defined through lim-ited statistical information extracted from 2D microstruc-ture snapshots. An accurate simulation of diffusion inrandom heterogeneous media has to satisfactorily accountfor the twin issues of randomness as well as the multi-length scale variations in the material properties. We pro-pose a general methodology to construct a data-driven,reduced-order microstructure representation model to de-scribe property variations in realistic heterogeneous media.This reduced-order model then serves as the input to theSPDE describing thermal diffusion through random het-erogeneous media. A decoupled scheme is used to tackle

146 CS07 Abstracts

the problems of stochasticity and multi-length scale vari-ations in properties. A sparse-grid collocation strategy isutilized to reduce the solution of the SPDE to a set of deter-ministic problems. A variational multiscale method withexplicit subgrid modeling is used to solve these determin-istic problems. An illustrative example using experimentaldata is provided to showcase the effectiveness of the pro-posed methodology.

Nicholas ZabarasMechanical and Aerospace EngineeringCornell Universityzabaras@cornell.edu

Baskar GanapathysubramanianCornell Universitybg74@cornell.edu

MS90

Arbitrary Order Accurate and UnconditionallyStable Discretization of the 4D Navier-StokesEquation on Unstructured Meshes

Stablized numerical methods utilizing continuous and dis-continuous basis approximations are presented for dis-cretizing the time-dependent compressible Navier-Stokesflow equations about curved geometries using arbitrarymesh complexes containing simplex, brick, prism, andpyramidal elements. Salient features of this formulationand implementation include: (1) arbitrary order accuracyin both space and time (for sufficiently smooth solutions)using machine generated basis representations, (2) prov-able global nonlinear stability whenever entropy convexityis strictly retained, and (3) parallel implementation usingdomain decomposition techniques. Numerical results forcompressible Navier-Stokes flow are presented to illustrateperformance characteristics of the method(s).

Timothy J. BarthNASA Ames Research CenterTimothy.J.Barth@nasa.gov

MS90

Accuracy of Mixed-Element Finite-Volume Dis-cretizations

The recent drag prediction workshops have identified lackof reliable accuracy analysis for unstructured discretiza-tions as a critical problem. This paper proposes a unifiedapproach to evaluating accuracy of finite-volume discretiza-tions on mixed-element unstructured grids. The analysisis applied to the inviscid-flow equations discretized witha typical node-based discretization; the first-order conver-gence on mixed grids is shown and explained. Alternativediscretizations, demonstrating convergence with the sec-ond and third designed accuracy order, are analyzed andtested.

Boris DiskinNational Institute of Aerospace, Hampton, VAbdiskin@nianet.org

James ThomasNASA Langley Research CenterHampton, VAjames.a.thomas@nasa.gov

MS90

Simulation of Heating on Unstructured Grids inHypersonic Flows

The quality of surface heat transfer simulation under con-ditions of hypersonic flow as a function of flux reconstruc-tion algorithm within FUN3D is reviewed. Focus is onall tetrahedral elements in order to preserve flexibility forgrid adaptation and remove constraints of semi-structured(prismatic) grids across all shear layers. Context for discus-sion is provided by a simple test case (flow over a cylinder)and a more complex case (flow over a spacecraft towing atoroidal ballute).

Peter A. GnoffoNASA Langley Research CenterPeter.A.Gnoffo@nasa.gov

MS90

Paths Toward Accurate Unstructured Grid Heat-ing

An account of trials and tribulations endured during thequest for predicting aeroheating with unstructured grids.

Bil KlebNASA LangleyBil.Kleb@NASA.gov

MS90

Newton-Krylov Methods on Unstructured Meshesfor Aerodynamic Flows

In this presentation two Newton-Krylov algorithms aredescribed for solution of the compressible Navier-Stokesequations on unstructured meshes. In the first, the mean-flow equations are fully coupled with the turbulence modelequation; in the second algorithm, the two systems areloosely coupled. Both algorithms use the generalized min-imal residual Krylov solver with incomplete lower-upperpreconditioning. Results are presented for several two- andthree-dimensional flows, including a wing-body-nacelle ge-ometry.

David W. ZinggUniversity of Toronto Institute for Aerospace Studiesdwz@oddjob.utias.utoronto.ca

P. Wong, M. BlancoUniversity of TorontoInstitute for Aerospace Studiespw@oddjob.uias.utoronto.ca, mb@oddjob.uias.utoronto.ca

MS91

Phase Field Modeling and Simulation of Some In-terface Problems

We present our on-going works on the phase field modelingand simulations of some interface problems, ranging frommicrostructure evolution in multicomponent alloy to lipidvesicle deformation and interaction in fluid. We discussrecent development of highly adaptive computational al-gorithms for large scale phase field simulations. We alsoaddress how to effectively retrieve useful statistical infor-mation within the phase field framework.

Qiang DuPenn State University

CS07 Abstracts 147

Department of Mathematicsqdu@math.psu.edu

MS91

Rayleigh-Taylor Turbulent Mixing

Improvements to the Front Tracking method have in-creased its power and ease of use. The robust treatmentof bifurcations was achieved through combination of therobust but less accurate grid based tracking with the accu-rate but less robust grid free tracking. This, with improvedphysical modeling (correct modeling of physical transportphenomena, etc.), allows validation of simulations for the3D Rayleigh-Taylor chaotic mixing problem. We thank themany collaborators who contributed to this work.

James G. GlimmSUNY at Stony BrookDept of Applied Mathematicsglimm@ams.sunysb.edu

MS91

Regularization for Accurate Numerical Wave Prop-agation in Discontinuous Media

Structured computational grids are the basis for highlyefficient numerical approximations of wave propagation.When there are discontinuous material coefficients the ac-curacy is typically reduced and there may also be stabilityproblems. In this talk, we consider a technique for modify-ing the material coefficients close to the material interface,to improve on the order of accuracy of the Yee scheme aswell as other (also higher order) methods based on a similarstaggered structure.

Anna-Karin TornbergCourant Institute of Mathematical SciencesNew York Universitytornberg@cims.nyu.edu

MS91

An Eulerian Formulation for Interfacial Flows withSurfactant

An interfacial flow with surfactant involves more compli-cated physics along the interface as well as more compli-cated coupling of interface dynamics and bulk dynamics.An Eulerian framework is developed to capture both thesurfactant distribution on the interface, the moving inter-face, and the ambient fluid flow. Extensive computationresults will be shown to validate our algorithm. This is ajoint work with Z. Li, J. Lowengrub and J. Xu.

Hongkai ZhaoUniversity of California, IrvineDepartment of Mathematicszhao@math.uci.edu

MS92

Speaker Names

To Be Announcedtbatba

MS93

Shape Determination for Real and ComplexMaxwell Eigenvalue Problems

Experimentally observed cavity response differ from thatof ideal cavity. This is due to shape deviations resultingfrom both loose machine tolerance in the fabrication, andtuning process for the accelerating mode. In this talk, wepresent a shape determination algorithm to solve for theunknown cavity deviations using the real cavity’s frequencyresponse. The inverse problem is posed as a least-squaresminimization problem. Nonlinear optimization problemis solved using a line search based reduced space Gauss-Newton method, and shape sensitivities are computed witha discrete adjoint approach. We present both real-life andsynthetic examples.

Volkan Akcelik, Lie-Quan Lee, Kwok KoStanford Linear Accelerator Centervolkan@slac.stanford.edu, liequan@slac.stanford.edu,kwok@slac.stanford.edu

MS93

Shape Optimization in Support of ImplantableBlood Pump Design

Several challenges and methods in biomedical flow devicedesign are described. The objective often involves theunique behavior of blood as the flowing medium, neces-sitating, e.g., accurate modeling of cell damage. The com-plex constitutive behavior, in particular shear-thinning,may affect the outcome of shape optimization more thanit affects direct flow analysis. Finally, target applicationsoften involve intricate time-varying geometry, and thus, re-alistic solutions can be only obtained on high-performanceparallel computers.

Markus Probst, Marek BehrRWTH Aachen UniversityChair for Computational Analysis of Technical Systemsprobst@cats.rwth-aachen.de, behr@cats.rwth-aachen.de

Mike NicolaiRWTH Aachen Universitynicolai@cats.rwth-aachen.de

MS93

Optimization of Self-Stability for Periodic Motionof Walking and Running Robots

Abstract not available at time of publication.

Georg BockIWRUniversity of Heidelbergbock@iwr.uni-heidelberg.de

MS93

Determination of Initial Orbits of Satellites AfterFaulty Launches

Abstract not available at time of publication.

Ekaterina KostinaIWR - University of Heidelbergekaterina.kostina@iwr.uni-heidelberg.de

148 CS07 Abstracts

MS94

Preconditioned Iterative Solvers for Linear Stabil-ity Analysis of Incompressible Flows

We explore iterative methods for eigenvalue problemsA� = λB� arising from linear stability analysis of theNavier-Stokes equations. A is a nonsymmetric indefinitematrix with structure like that of saddle point systemsand B is singular. The matrix-vector products required bymethods such as inverse iteration or the implicitly restartedArnoldi algorithm entail solution of linear systems withcoefficient matrix A or A − θB. For this, we use precon-ditioned Krylov subspace methods and examine effects ofReynolds number and shifts on performance. Moreover, westudy “inexact” solvers and the effects of stopping criteriaon the performance and costs of eigenvalue computations.

Howard C. ElmanUniversity of Maryland, College Parkelman@cs.umd.edu

MS94

The Effect of Inner Solver Accuracy and BoundaryConditions on Pressure Convection-Diffusion Pre-conditioners for the Incompressible Navier-StokesEquations

While nu-merous studies have demonstrated mesh-independent con-vergence for Pressure Convection–Diffusion precondition-ers and their overall efficacy, several potential weaknessesremain in their practical use. The relationship betweenaccuracy of inner sub-problem solves and overall conver-gence rate of the outer iteration is not well understood forthe Navier-Stokes equations or when the inner sub-blocksolver has less than ideal behavior. We discuss this issueas well as the influence of boundary conditions on overallalgorithm convergence.

Victoria E. HowleSandia National Laboratoriesvehowle@sandia.gov

MS94

Two-Phase Incompressible Flow Problems: Dis-cretization and Preconditioners

In this talk we consider a standard model for a two-phaseflow problem, namely the incompressible Navier-Stokesequations with a localized force term at the interface be-tween the two phases. The levelset approach is used forthe implict representation of the interface. Special finiteelememt spaces are used for discretization. We presentpreconditioning methods that have robustness propertieswith respect to mesh size, time step and jumps in problemparameters (density and viscosity).

Arnold ReuskenNumerical MathematicsRWTH Aachen University, Aachen, Germanyreusken@igpm.rwth-aachen.de

MS94

Least Squares Commutator Preconditioning forStabilized Mixed Approximation

The focus of this talk is the Least Squares Commutator(LSC) preconditioner developed by Elman, Howle, Sha-did, Shuttleworth and Tuminaro. The original version of

the preconditioner required that the underlying spatial dis-cretization be uniformly inf-sup stable. Here the definitionof the original preconditioner is generalized to cover thecase of discrete systems that arise when using stabilizedlow-order mixed finite element approximation or collocatedfinite difference methods.

David SilvesterSchool of MathematicsUniversity of Manchester, Manchester, UKd.silvester@manchester.ac.uk

MS95

Continuation of Sparse Eigendecompositions

The eigenvalues of large parameter-dependent matricesprovide insight to engineers designing resonators and tothose studying the stability of dynamical equilibria. Wedescribe continuation methods for approximating a feweigenvalues of such parameter-dependent matrices. In par-ticular, we explore how the continuous structure of theseproblems informs the choice of solver parameters at eachstep, and how information from the eigensolver can be usedto make choices about step size control in the continuationprocess.

David BindelCourant Institute of Mathematical SciencesNew York Universitydbindel@cims.nyu.edu

Mark J. FriedmanUniversity of AlabamaDepartment of Mathematicsfriedman@math.uah.edu

MS95

Continuation for the Ornstein-Zernike EquationUsing LOCA

The Ornstein-Zernike equation together with a closureequation can be solved to find probability distributions ofatoms in fluid states. Varying parameters of the state suchas density and temperature allows us to understand phasetransitions, say, from liquid to vapor. It has been shown,however, that such a continuation study produces incorrectresults when using a common closure equation. We seekto perform this study using an alternative closure equationusing the software LOCA.

B.M. Pettitt, M. MaruchoUniversity of Houstonpettitt@uh.edu, marucho@kitten.chem.uh.edu

A.G. SalingerSandia National Laboratoriesagsalin@sandia.gov

C.T. KelleyNorth Carolina State Univtim kelley@ncsu.edu

Kelly DicksonNorth Carolina State Universitykidickso@ncsu.edu

MS95

Computing Hopf Bifurcations in Large-Scale Prob-

CS07 Abstracts 149

lems

Hopf bifurcations, signified by the birth of an oscillatoryperiodic solution, are a common means by which dynamicalsystems become unstable. Examples include flutter, vor-tex shedding, and chemical oscillators. We describe blockelimination and bordered matrix methods for computingHopf bifurcations that are scalable to problems with mil-lions of unknowns. These methods have been implementedin LOCA, part of the Trilinos solvers collection, and aredesigned to be easily integrated into existing engineeringcodes.

Andrew SalingerApplied Computational Methods Dept, Sandia NationalLabsagsalin@sandia.gov

Eric PhippsSandia National LaboratoriesApplied Computational Methods Departmentetphipp@sandia.gov

MS95

Periodic Orbit Tracking for Large-Scale Applica-tions

A general-purpose periodic orbit tracking capability is be-ing developed in Sandia’s Trilinos framework. We use fi-nite difference discretizations of the time domain and usea Newton’s method to solve the entire space-time prob-lem. Parallelism over the space and time domains is im-plemented, and different preconditioning strategies are in-vestigated. For 3D PDE applications, this formulation isfor a ”steady” problem in four dimensions, so existing con-tinuation and stability analysis capabilities can be used.

Andrew SalingerSandia National Labsagsalin@sandia.gov

MS96

Deformable Boundaries on Moving Overset Grids

We consider viscous flow coupled to deformable bound-aries. We introduce “essentially Cartesian grid methods”where thin unstructured grids track the deformable bound-aries while most of the domain is covered by structuredCartesian grids. This is the natural extension of classicaloverset (Chimera) schemes which simplifies the treatmentof complex surface geometry. Computational examples arepresented to illustrate the new features of these algorithms.

Petri FastCenter for Applied Scientific ComputingLawrence Livermore National Laboratorypfast@llnl.gov

MS96

Turbulent Mixing in ImplodingRichtmyer-Meshkov Instability

We study imploding Richtmyer-Meshkov instability to un-derstand the effect of the numerical flow model on late timemixing dynamics, in particular sharp interfaces vs. mixedcell pressure-temperature equilibrium. For early times themodels behave similarly, but show completely different latetime mixing structures. Mixed cell treatments are domi-nated by a few fully mixed well defined vortices, while sharp

interface treatments show fragmented materials with largetemperature spikes and a many fine scale vortices.

Thomas MasserContinuum Dynamics Group, CCS-2CCS Division, Los Alamos National Laboratorytmasser@lanl.gov

John W. GroveMethods for Advanced Scientific Simulations GroupContinuum Dynamics Group, CCS-2jgrove@lanl.gov

MS96

Numerical Algorithms for MHD of Free SurfaceFlows of Ablated Materials

New mathematical models, algorithms, and computationalsoftware have been developed for the study of magnetohy-drodynamics of multiphase flows in the presence of phasetransitions. The code is applicable to the simulation of freesurface flows of electrically conducting liquids or weaklyionized plasmas ablated by particle or laser beams in mag-netic fields. Applications of the developed methods forthe simulation of tokamak fueling through the injection ofsmall frozen deuterium - tritium pellets will be discussed.We have performed first systematic studies of the pelletablation in magnetic fields, and our results disproved someprevailing expectation about the role of the geometry andmagnetic field on the pellet ablation rate.

Paul ParksGeneral Atomicsparks@fusion.gat.com

Tianshi LuBrookhaven National Laboratorytlu@bnl.gov

Jian DuStony Brook Universityjidu@ams.sunysb.edu

Roman V. SamulyakBrookhaven National Laboratoryrosamu@bnl.gov

MS96

Application of the PPB Moment-Conserving Ad-vection Scheme to Multifluid Interface InstabilityProblems

A moment-conserving finite difference scheme for nonlin-ear advection, the PPB scheme, has been derived from anextension to 3D of van Leers Scheme VI and with the addi-tion of appropriate constraint conditions. This scheme willbe briefly described along with its implementation insidethe PPM gas dynamics scheme. A variety of multifluid in-terface instability problems have been attacked using thisPPM/PPB combination, including problems with severaldistinct fluids. These results will be presented and the ad-vantages of this approach discussed.

David Porter, Paul R. WoodwardLaboratory for Computational Science and EngineeringUniversity of Minnesotadhp@lcse.umn.edu, paul@lcse.umn.edu

150 CS07 Abstracts

MS97

Convergence of Pseudospectral Methods for Non-linear Optimal Control Problems

A main problem in control engineering is solving a con-strained nonlinear optimal control problem. In recentyears, many practical, nonlinear optimal control problemshave been solved by pseudospectral (PS) methods. In aneffort to better understand the PS approach to solvingcontrol problems, we present some convergence results forproblems with mixed state and control constraints. It isproved that the PS-discretized optimal control problem isa consistent approximation to the continuous-time optimalcontrol problem. Convergence can be guaranteed undernumerically verifiable conditions.

Qi GongUniversity of Texas at San AntonioQi.Gong@utsa.edu

MS97

Convergence of a Curse-of-Dimensionality-FreeMethod for HJB PDEs

A nonlinear HJB PDE corresponding to an infinite time-horizon control problem is used as a basis for developmentof a curse-of-dimensionality-free numerical method. In par-ticular, the method handles PDEs which are written as (orwell-approximated by) a point-wise maximum of quadraticHamiltonian forms. The approach works by exploiting thestructure of the semiconvex dual of the associated semi-group as an approximate max-plus summation of max-plusintegral operators with quadratic kernels. The solution isobtained over the entire space, with errors in the gradientgrowing linearly with distance from the origin. Previousresults have demonstrated that the computational growthas a function of space dimension is cubic (rather than ex-ponential). The downside is a curse-of-complexity whichis best dealt with via various pruning schemes includinga convex-programming approach. Convergence rates as afunction of the number of iterations will be discussed.

William M. McEneaneyDepts. of Math. and of Mech. and Aero. Eng.University of California, San Diegowmceneaney@ucsd.edu

MS97

Trajectory Optimization using Higher Order Im-plicit Integration Methods

Trajectory optimization is key to the design and analysisof aerospace vehicles. The use of implicit integration com-bined with modern nonlinear programming packages hasproven to be an effective technique for trajectory optimiza-tion. The development of higher order implicit integrationschemes will be covered. Computation experiences apply-ing these methods to aircraft and interplanetary spacecraftproblems will be shared.

Stephen ParisBoeing Phantom Worksstephen.w.paris@boeing.com)

MS97

Addressing Dimensionality and Complexity Cursesin Computational Optimal Control

The Hamilton-Jacobi framework for solving optimal con-

trol problems suffers from Bellmans famous curse of di-mensionality. It can be easily argued that the Pontryaginframework suffers from a curse of complexity arising fromthe symplectic structure of the Hamiltonian system. It ispossible to delay the onset of dimensionality and complex-ity by modern computational techniques whose roots canbe traced back to the original ideas of Bernoulli and Eu-ler. This talk will explore these issues thru the prism ofnew insights brought on by the availability of extraordinarycomputational power on ordinary computers.

Michael RossDepartment of Mechanical and Astronautical EngineeringNaval Postgraduate Schoolimross@nps.edu

MS98

Linear Systems Arising in Computational Geome-chanics

Finite element analysis is widely used in engineering ge-omechanics. Most problems require solutions of linear sys-tems which are often both very large and include the effectsof nonlinear material behaviour. This talk will provide anoverview of the types of systems generated and will high-light some of the outstanding research issues in this area.

Alison RamageDept of MathematicsUniversity of Strathclydealison@maths.strath.ac.uk

Charles E. AugardeDurham UniversitySchool of Engineeringcharles.augarde@durham.ac.uk

MS98

An Element-by-Element Krylov Solver for Dy-namic Soil-Structure Interaction

The survivability against aircraft impact of a nuclear con-tainment vessel sited on soft soils poses a challenging dy-namic soil-structure interaction problem. The foundationstiffness plays a key role in controlling the stresses expe-rienced by the superstructure. Here the efficient use ofthe Scaled Boundary Element method (to simulate the dy-namic far-field) in conjunction with a Krylov element-by-element NLFE solver is examined. Particular attention isgiven to reducing compute time when calculating the con-volution integral.

Roger CrouchDurham UniversitySchool of Engineeringr.s.crouch@durham.ac.uk

MS98

Block Preconditioners for FE Coupled Consolida-tion Equations

The repeated solution in time of the large size indefinitelinear system resulting from the FE integration of coupledconsolidation equations is a major computational effort.Because of ill-conditioning, a suitable preconditioner is nec-essary to guarantee the convergence of projection methodsbased on Krylov’s subspaces. Novel block preconditionersare theoretically investigated with their practical applica-

CS07 Abstracts 151

tion discussed. Several numerical tests show their efficiencyand robustness as compared to standard ILU/ILUT pre-conditioners.

Massimiliano Ferronato, Giuseppe GambolatiUniversity of PadovaDMMMSAferronat@dmsa.unipd.it, gambo@dmsa.unipd.it

Luca BergamaschiUniversita di PadovaItalyberga@dmsa.unipd.it

MS98

Element-Based Preconditioners for Problems inGeomechanics

The solution of algebraic equilibrium equations lies at theheart of a nonlinear finite element analysis in geotechnicalengineering. This problem is usually reduced to a sequenceof large sparse linear system solves, so iterative solvers andpreconditioners play important roles. Here we review theuse of a range of established element-based preconditionersfor linear elastic and elasto-plastic problems and comparetheir performance with a new element-based method whichoffers a significant improvement in performance.

Charles E. AugardeDurham UniversitySchool of Engineeringcharles.augarde@durham.ac.uk

Alison RamageUniversity of StrathclydeA.Ramage@strath.ac.uk

Jochen StaudacherUniversity of Durhamjochen staudacher@yahoo.de

MS99

Title Not Available at Time of Publication

Abstract not available at time of publication.

Michael BowlingUniversity of Albertabowling@cs.ualberta.ca

MS99

Gaussian Processes in Trust-Region OptimizationMethods

Gaussian process models are often used to emulate expen-sive computer simulations. Recently, they have also beenused to model the ”error field” between two levels of fidelityin a computer simulation. This work examines the efficacyof using Gaussian processes in trust-region surrogate-basedoptimization. Since Gaussian processes account for uncer-tainties, they offer a potentially powerful way to reduce thenumber of high-fidelity function evaluations necessary inmulti-fidelity optimization, especially in optimization prob-lems which include uncertainty.

Laura SwilerSandia National LaboratoriesAlbuquerque, New Mexico 87185

lpswile@sandia.gov

Patty HoughSandia Nat’l Labspdhough@sandia.gov

MS99

Title Not Available at Time of Publication

Abstract not available at time of publication.

Andreas ZellEberhard-Karls-Universitat Tubingenzell@informatik.uni-tuebingen.de

MS100

Why Advanced PDE Frameworks Should Use aDomain-Specific Language

Application codes need reusable components for meshes,solvers, and different physical components. However, manyimportant processes are governed by PDE. By introducinga domain-specific language for PDE, it is possible to gener-ate many such physical components while still interfacingto a common set of meshes and solvers. Moreover, layeringphysical components on top of such a unified approach toPDE allows a single entry point for fast algorithms or ad-vanced approximating functions to be shared across phys-ical modules. I will present examples of this concept fromthe FEniCS project and Sundance.

Robert KirbyTBDTBDrobert.c.kirby@ttu.edu

MS100

Building High-performance, Optimization-EnabledPDE Simulations with Sundance

The Sundance high-level components allow building high-performance parallel PDE simulations with a convenientsymbolic problem description language, also enabling ad-vanced algorithms for PDE-constrained optimization anduncertainty quantification. The symbolic problem descrip-tion also facilitates automated performance optimizationsthrough which Sundance-built simulators can get runtimeperformance that is often superior to hand-coded domain-specific PDE codes. We will describe the symbolic engine’sdesign, the architecture enabling its use with other frame-works, and show applications case studies.

Kevin LongSandia National Laboratorieskrlong@sandia.gov

MS100

Automatic Parallelization with Hybrid Analysis

Hybrid Analysis (HA) compiler technology can seamlesslyintegrate static and run-time analysis of memory refer-ences into a single framework that can perform data de-pendence analysis and generate necessary information formost memory related optimizations. HA is used for auto-matic parallelization of programs. It extracts run-time as-sertions from loops and generates minimum overhead run-time tests. The technology has been implemented in thePolaris compiler and has parallelized 22 benchmark codes

152 CS07 Abstracts

with 99% coverage and scalable speedups.

Lawrence RauchwergerComputer Science DepartmentTexas A&M Universityrwerger@cs.tamu.edu

MS100

Plug-n-Play Linear Solvers: Abstraction of LinearSystem Assembly

Sparse linear systems arise in many engineering applica-tions, and their solution often dominates runtime. Opti-mal linear system solution can be highly problem specific,which motivates the need to switch among various solverlibraries. Widely varying solver interfaces makes switchingdifficult, so we have developed abstraction layers that en-capsulate solver-library-specific interfaces and data types.The process of assembling and manipulating linear systemswill be described, as well as access to solution methods andother operations.

Alan B. WilliamsSandia National LaboratoryDistributed Systems Research Departmentwilliam@sandia.gov

MS101

Enabling and Comparing Weak to Strong Multi-physics Coupling

This talk addresses development of stronger coupling al-gorithms approaching monolithic coupling using as littleproblem information beyond weak coupling as possible.Candidate algorithms involve matrix-free and Broyden-based approaches. Practical realization of these algo-rithms via solver libraries is discussed. The relative perfor-mance and cost associated with the various algorithms iscomapred leading to an understanding of (dis)advantagesand appropriate use. Examples ranging from coupled pro-totype systems to coupled production scale analysis codeswill be presented.

Roger PawlowskiSandia National Labsrppawlo@sandia.gov

Russell W. HooperSandia National Laboratoriesrhoope@sandia.gov

MS101

Algorithmic and Numerical Aspects of CoupledProblems

Coupled problems arise naturally in many areas, such asfluid-structure interaction. Often, there are good meth-ods for each single problem. This leads to a partitionedapproach. Here one wants to obtain the same results asfully monolithic. Assuming solvers for each subproblem,we look at numerical methods to solve the coupled prob-lem, explaining some effects. Aditionally, we consider theseparate pieces of subproblem software as components in asoftware engineering sense.

Hermann G. Matthies, Rainer NiekampInstitute of Scientific ComputingTechnical University BraunschweigH.Matthies@tu-bs.de, r.niekamp@tu-bs.de

MS101

Globalization-Preserving Coupling Techniques forCircuit-Device Coupling

This talk presents an algorithm to solve coupled circuitsimulation between a low-fidelity lumped parameter circuitsimulator and a high-fidelity PDE simulatior for drift dif-fusion. Each code is highly nonlinear and requires specificGlobalized Newton-based techniques. Each application’sglobalization is incompatible with the other. Strong androbust coupling is achieved using a nonlinear eliminationtechnique that preserves each application’s globalizationtechnique. Results will be shown for large-scale parallelcircuits using production codes at Sandia.

Roger PawlowskiSandia National Labsrppawlo@sandia.gov

MS101

Modular Coupling Strategies for Melt CrystalGrowth Models

We desire to construct a model for melt crystal growth pro-cesses that is both computationally expedient and math-ematically self-consistent by employing codes that solvenonlinear, boundary value problems coupled along a com-mon domain boundary. We present several strategiesto implement a loose coupling of such codes. A blockGauss–Seidel iteration procedure is simple to implementbut not robust. Much more promising is an approximate,Block-Newton approach implemented using a Jacobian-freeNewton-Krylov algorithm.

Lisa LunChemical Engineering & Materials ScienceUniversity of Minnesotalun@cems.umn.edu

Jeffrey J. DerbyDept. of Chemical Engineering & Materials ScienceUniversity of Minnesotaderby@umn.edu

Andrew YeckelUniv. of Minnesotayecke003@umn.edu

MS102

MKL Intel’s Numerical Library on Multicore

Greg HenryIntel Corporationgreg.henry@intel.com

MS102

Solving Dense Symmetric Positive Definite Sys-tems of Linear Equations Using Cholesky Factor-ization on the CELL Processor

We present a mixed-precision algorithm for solving sym-metric positive definite systems of linear equations on theCELL processor. The algorithm is based on Cholesky fac-torization in single precision and iterative refinement ofthe single precision result to achieve double precision accu-racy. Parallel Cholesky factorization is based on pipeliningof consecutive steps of the algorithm in order to achieve

CS07 Abstracts 153

excellent load balance and almost complete hiding of com-munication latency.

Jakub KurzakInnovative Computing LaboratoryUniversity of Tennesseekurzak@cs.utk.edu

MS102

Extra-Precise Iterative Refinement for LeastSquares Problems

We present the algorithm, error bounds, and numerical re-sults of the extra-precise iterative refinement for overdeter-mined linear least squares (LLS) problems. We apply ourlinear system refinement algorithm to Bjorck’s augmentedlinear system formulation of the LLS problem. Our algo-rithm reduces the forward normwise and componentwiseerrors to

√nε unless the system is too ill-conditioned. In

contrast to linear systems, we provide two separate errorbounds for the solution x and the residual r.

Jason RiedyUniversity of California, BerkeleyDivision of Computer Scienceejr@cs.berkeley.edu

Xiaoye S. LiComputational Research DivisionLawrence Berkeley National Laboratoryxsli@lbl.gov

James W. DemmelUniversity of CaliforniaDivision of Computer Sciencedemmel@cs.berkeley.edu

Yozo HidaUniv. of CaliforniaBerkeleyyozo@cs.berkeley.edu

MS102

LAPACK For Clusters: Productivity Meets HighPerformance

LAPACK For Clusters (LFC) allows seamless paralleliza-tion of numerically intensive computations through the fa-miliar environments such as Mathematica, MATLAB, andPython. These client environments naturally hide the in-herent complexity of the parallel code in their sequentialuser interface. The computational resources reside on theserver side in a form of a parallel cluster that allows remotemanipulation of distributed objects and execution of par-allel code. The integration between the server and clientenvironments happens through the standard function over-loading features of the clients and thus allows effortlessscaling of existing sequential codes as well as writing newalgorithms with the functionality of the server that extendsbuilt-in capabilities of the clients.

Piotr LuszczekUniversity of Tennessee KnoxvilleDepartment of Computer Scienceluszczek@cs.utk.edu

MS103

Inverse Seismic Wave Propagation

Inverse problems in seismic wave propagation are difficultto solve due to their highly nonlinear nature. A successfulstrategy here is to use multiscale hierarchies both in thespace discretization and the signal frequencies. Alterna-tively, experience from computational seismology suggeststo amend the misfit term by traveltime measurements ormore general integral transform operators. We combinethese ideas for the solution of inversion problems on realgeological data and provide a variety of numerical results.

Carsten BursteddeUniversity of Texas at Austincarsten@ices.utexas.edu

MS103

Dimensionality Reduction and Polynomial ChaosAcceleration of Bayesian Inference in Inverse Prob-lems

In the Bayesian setting for inverse problems, the cost oflikelihood evaluations with computationally intensive for-ward models may be prohibitive. This problem is com-pounded by high dimensionality, as when the unknown isa spatiotemporal field. We address these difficulties bycombining a Karhunen-Loeve representation of Gaussianprocess priors with a Galerkin/polynomial chaos construc-tion to propagate prior uncertainty through the forwardmodel. The result is a lower-dimensional surrogate poste-rior which may be explored at negligible cost.

Habib N. NajmSandia National LaboratoriesLivermore, CA, USAhnnajm@sandia.gov

Youssef M. MarzoukSandia National Laboratoriesymarzou@sandia.gov

MS103

Comparison of Advanced Large-Scale MinimizationAlgorithms for the Solution of Inverse Ill-PosedProblems

We compare performance of several robust large-scale min-imization algorithms applied for unconstrained minimiza-tion of cost functional in the solution of ill-posed inverseproblems applied to parabolized Navier-Stokes equations.The methods compared consist of the nonlinear conju-gate gradient method, BFGS, the limited memory Quasi-Newton (L-BFGS) , Truncated Newton method and a newhybrid algorithm . For all methods employed the gradi-ent of the cost function is obtained via an adjoint method.The hybrid method emerged as the best performer for anadequate choice of parameters controlling the number of L-BFGS and Truncated Newton iterations to be interlaced.

Ionel Michael NavonDepartment of Mathematics and C.S. I.T.Florida State Universitynavon@csit.fsu.edu

Aleksey AlekseevDepartment of Aerodynamics and Heat Transfer, RSC,ENERGIA,Korolev (Kaliningrad), Moscow Region 141070, Russia

154 CS07 Abstracts

aleksey.alekseev@relcom.ru

MS103

Real-Time Reliable Parameter Estimation for Sys-tems Described by Partial Differential Equations

We present a reduced-basis technique for the reliable real-time parameter estimation in parametrized partial differen-tial equations. We first formulate a parameter estimationproblem of identifying a compact set of all possible pa-rameter values consistent with the interval measurements.We then replace the truth approximation outputs with thereduced-basis output bounds to obtain a new problem for-mulation of several orders of magnitude lower computa-tional cost than the original problem. Finally, we proposeefficient algorithms to construct approximate bounding re-gions for the solution of the new problem. Numerical re-sults of a nondestructive evaluation problem is presentedto demonstrate several features of our approach.

Anthony T. Patera, M. A. GreplMassachusetts Institute of Technologypatera@mit.edu, martin grepl@yahoo.de

Gui-Rong LiuNational University of Singaporempeliugr@nus.edu.sg

Cuong NguyenMassachusetts Institute of Technologycuongng@mit.edu

MS104

Augmentation Preconditioners for Saddle PointSystems

In this talk we provide an overview of augmentationpreconditioners for saddle point systems of the form[A BT ;B 0]. Those preconditioners come in a few flavors.Defining W as a weight matrix, the basic form is block di-agonal, with A+BTW−1B in the (1,1) block and W in the(2,2) block. The preconditioned matrix has the interestingproperty that the higher the nullity of the (1,1) block is, thefaster a minimal residual Krylov solver (such as MINRES)converges. When the nullity of A is equal to the number ofconstraints, convergence (in the absence of roundoff errors)is expected to occur within two iterations. When appliedto discretized PDEs, it is desirable to exploit the proper-ties of the differential operators in a way that will allow forfast inversion of the augmented (1,1) block. This issue andother computational properties of the preconditioner willbe discussed.

Chen GreifUniversity of British ColumbiaCanadagreif@cs.ubc.ca

MS104

Augmented Lagrangian and Schur ComplementPreconditioners for the Oseen Equations

We discuss several block preconditioners for the discreteOseen system. In one group preconditioners make use ofspecial approximations to the pressure Schur complementof the problem. We will consider and compare several op-tions of building such approximations. To avoid construct-ing sophisticated pressure Schur complement approxima-

tions we further consider a block preconditioner for an aug-mented Lagrangian formulation of the corresponding sad-dle point system. In this approach the crucial ingredient isan appropriate solver for the (1,1) block of the system. Wediscuss available theoretical and numerical results for dif-ferent preconditioning techniques with respect to the meshand viscosity dependence. This presentation is based on ajoint research with M.Benzi.

Maxim OlshanskiiDepartment of Mechanics and MathematicsMoscow State M.V.Lomonosov University, Moscow,RussiaMaxim.Olshanskii@mtu-net.ru

MS104

Block Preconditioning for Stabilized Finite Ele-ments and Microfluidic Applications

Over the past several years, considerable effort has beenplaced on developing efficient solution algorithms for theincompressible Navier-Stokes equations. The effectivenessof these methods requires that the solution techniques forthe linear subproblems generated by these algorithms ex-hibit robust and rapid convergence. These methods shouldbe insensitive to problem parameters such as mesh size andReynolds number. This study concerns a class of precondi-tioners derived from a block factorization of the coefficientmatrix generated in a Newton nonlinear iteration for theprimitive variable formulation of the system. These pre-conditioners are based on the approximation of the Schurcomplement operator using a technique proposed by El-man, Howle, Shadid, Shuttleworth, and Tuminaro [H. El-man, V. Howle, J. Shadid, R. Shuttleworth, R. Tuminaro,Block Preconditioners Based on Approximate Commuta-tors, SIAM J. on Sci. Comp. 27 (2006) 1651 - 1668], Kay,Loghin, and Wathen [D. Kay, D. Loghin, and A. J. Wathen,A preconditioner for the steady-state Navier-Stokes equa-tions, SIAM J. on Sci. Comp. 24 (2002) 237-256.], and Sil-vester, Elman, Kay, and Wathen [D. Silvester, H. Elman,D. Kay, A. Wathen, Efficient preconditioning of the lin-earized Navier-Stokes equations for incompressible flow, J.Comp. Appl. Math. 128 (2001) 261-279.]. It is derived us-ing subsidiary computations (solutions of pressure Poissonand convection-diffusion-like subproblems) that are signif-icantly easier to solve than the entire coupled system, anda solver can be built using tools, such as smooth aggrega-tion multigrid for the subproblems. We discuss two com-putational studies we performed using MPSalsa, a stabi-lized finite element code, and Sundance, a high-level sym-bolic differentiation finite element code. Using MPSalsa,we compare parallel versions of the pressure convection-diffusion preconditioners with an overlapping Schwarz do-main decomposition preconditioner. Using Sundance, weapply these techniques to realistic microfluidic problemswhere the flow is driven by an electric potential field. Ourresults show nearly ideal convergence rates for a wide rangeof Reynolds numbers with both enclosed and in/out flowboundary conditions on both structured and unstructuredmeshes.

Robert ShuttleworthCenter for Scientific Computation And MathematicalModelingUniversity of Maryland, College Park, MDrshuttle@math.umd.edu

MS104

High-Order-in-Time Factorizations for Solving and

CS07 Abstracts 155

Preconditioning the Incompressible Navier-StokesEquations

Algebraic Yosida-like fractional-step methods for solvingthe unsteady Navier-Stokes equations are presented. Thesemethods (Quarteroni, Saleri, Veneziani, J Math Pur Appl,1999, Saleri, Veneziani, SIAM J Num An, 2004, Gerva-sio, Saleri, Veneziani, J Comp Phys 2005) rely on approxi-mate LU block factorizations of the matrix of the discreteNavier-Stokes system. We address time accuracy of theseschemes and performances as preconditioners of the cou-pled Navier-Stokes system, using both finite elements andspectral space discretizations.

Alessandro VenezianiModeling and Scientific Computing,Dipartimento diMatematicaPolitecnico di Milano, Milano, Italyalessandro.veneziani@mate.polimi.it

Fausto SaleriMOX Department of MathematicsPolitecnico di Milanofausto.saleri@mate.polimi.it

Paola GervasioDipartimento di Matematica,Facolta di IngegneriaUniversita degli Studi di Bresci, Brescia, Italygervasio@ing.unibs.it

MS105

Improved Boundary Conditions for Electromag-netic Particle-in-Cell Algorithm

Particle-in-cell (PIC) calculations based on the electromag-netic finite-difference time-domain method (FDTD) aresimple, robust, and successful. However, the structured,Cartesian grids employed by the FDTD method resultin staircase approximations that cannot accurately modelcurved surfaces. We will compare the accuracy of Cartesiangrids, cylindrical grids, and a cut-cell embedded boundary.The particle currents must be weighted to these grids ina charge conserving manner. The charge conserving cur-rent weights are derived from finite element method (FEM)vector (edge) basis functions for the Cartesian (well knownVillasenor-Buneman current weights), cylindrical, and cut-cell embedded boundary.

Andrew GreenwoodAir force Research Laboratoryandrew.greenwood.kirtland.af.mil

Matthew T. BettencourtAir Force Research LaboratoryDEHEmatthew.bettencourt@kirtland.af.mil

Keith L. CartwrightAir Force Research Laboratorykeith.cartwright@kirtland.af.mil

MS105

Lagrangian and SemiLagrangian Models of Break-down

Simulation of breakdown presents computational chal-lenges because of the wide variation in spatial and tem-poral scales, and the need to keep numerical diffusion toan absolute minimum. We discuss attempts to develop

a very accurate fully Lagrangian (mesh-free) approach.Semi-Lagrangian approaches which are faster and attemptto achieve the accuracy of the particle simulation are alsodiscussed.

Nick HitchonUniversity of WisconsinElectrical and Computer Engineeringwhitchon@yahoo.com

MS105

Grid-Free Particle Simulations for ElectrostaticPlasmas

A grid-free particle method for electrostatic plasma simu-lations is presented. The method employs techniques fromvortex methods in computational fluid dynamics including:(1) treecode algorithm for evaluating the electric field in-duced by a set of point charges, (2) kernel smoothing tohandle the Coulomb singularity, and (3) adaptive particleinsertion to maintain resolution of the charge distribution.Simulations are presented for the instability of collisionlesselectron beams. This work is supported by AFOSR andNSF.

Benjamin SondayPrinceton Universitybsonday@math.princeton.edu

Robert KrasnyUniversity of MichiganDepartment of Mathematicskrasny@umich.edu

Lyudmyla BarannykUniversity of Michiganbarannyk@umich.edu

Andrew J. ChristliebMichigan State UniverityDepartment of Mathematicschristlieb@math.msu.edu

MS105

Recent Applications of 3D Finite-Element Analysisfor Electrostatic and Magnetostatic PIC

MICHELLE is a new two-dimensional and three-dimensional steady-state and time-domain particle-in-cell(PIC) code that employs electrostatic and now magneto-static finite-element field solvers. Over the past severalyears the code has been employed successfully by indus-try to design and analyze a wide variety of devices thatinclude multistage depressed collectors, electron guns, andion thrusters. This paper will present applications of theMICHELLE code, including parametric optimization fordesign applications.

John PetilloScience Applications International Corporationjpetillo@bos.saic.com

Baruch LevushNaval Research Laboratorybaruch.levush@nrl.navy.mil

MS106

Additive Schwarz Methods for Stochastic Elliptic

156 CS07 Abstracts

Equations

We present a parallel multilevel domain decomposition pre-conditioned recycling Krylov subspace method for the nu-merical solution of elliptic equations with stochastic uncer-tainties in the operator. Karhunen-Loeve expansion andGalerkin method with double orthogonal polynomial ba-sis are used to transform the stochastic problem into asequence of deterministic equations. We report results ob-tained from a PETSc based parallel implementation of arecycling Krylov subspace method preconditioned with theadditive Schwarz method.

Chao Jin, Congming LiDept. of Applied MathematicsUniversity of Colorado, Boulderchao.jin@colorado.edu, cli@colorado.edu

Xiao-Chuan CaiUniversity of Colorado, BoulderDept. of Computer Sciencecai@cs.colorado.edu

MS106

Solving the Stochastic Steady-State DiffusionProblem Using Multigrid

We study multigrid for the stochastic steady-state diffu-sion problem where the diffusion coefficient has a finiteKarhunen-Loeve expansion. The problem is discretized inspace using linear finite elements and in the “stochasticcomponent” with a polynomial chaos method. The result-ing discrete system is solved using multigrid where the spa-tial discretization varies from grid to grid while the stochas-tic discretization is held constant. We establish a “text-book” multigrid convergence rate independent of spatialmesh size, and we demonstrate performance with exper-iments. In addition, we explore extension of these ideasto the case where the diffusion equation is posed as a firstorder system discretized by mixed methods.

Howard C. ElmanUniversity of Maryland, College Parkelman@cs.umd.edu

Darran FurnivalUniversity of Marylandfurnival@cs.umd.edu

MS106

Adaptive Multi-Element Collocation Method forFlow Problems

Abstract not available at time of publication.

George KarniadakisBrown Universitygk@dam.brown.edu

MS106

Stochastic Galerkin Method for Elliptic Spdes: AWhite Noise Approach

We present and explain several advantages of using theWhite Noise probability space as a natural framework forthis problem. Applying properly the Wiener-Ito Chaos de-composition and a modification of the Karnunen-Loeve ex-pansion, we obtain statistically stationary log normal per-

meability field and symmetric positive definite linear sys-tem of equations whose solutions are the coefficients of aGalerkin-type approximation to the solution of the originalequation.

Marcus SarkisIMPA and WPImsarkis@impa.br

MS107

Parallel Adaptive Methods and Domain Decompo-sition

We discuss a parallel adaptive meshing strategy due toBank and Holst. The main features are low communicationcosts, a simple load balancing procedure, and the abilityto develop parallel solvers from sequential adaptive solverswith little additional coding. In this talk we will discusssome recent developments, including variants of the basicadaptive paradigm, improvements in the adaptive refine-ment algorithm itself, and a domain decomposition linearequations solver based on the same principles.

Randolph E. BankUniv of California - San DiegoDepartment of Mathematicsrbank@ucsd.edu

MS107

Adaptive Methods for Time-Dependent ProblemsUsing Classical and Adjoint Approaches

Global error control for initial value problems relies on pre-dicting the impact of accumulated error as it evolves intime. Methods based on Adjoint methods offer an attrac-tive but potentially expensive solution. The alternativeis to consider simple classical global error estimation forthe forward PDE problem. Both these approaches are de-scribed and compared and an attempt made to undertsandwhen one method should be used rather than the other.

Christopher E. GoodyerUniversity of Leedsceg@comp.leeds.ac.uk

Martin Berzins, Le-Thuy TranSCI InstituteUniversity of Utahmb@sci.utah.edu, ltran@cs.utah.edu

MS107

Convergence of Adaptive Methods with Applica-tions in Physics and Geometric Analysis

We consider two-scale models of electrostatics in biolog-ical materials, and similar nonlinear problems arising ingeometric analysis. We establish well-posedness and de-rive max-norm estimates. We then prove similar resultsfor Galerkin approximations, and use these results to de-rive a priori and a posteriori error estimates. We describean adaptive algorithm and prove convergenece for the firstmodel, and indicate the obstacles for a similar result forthe second. We finish with examples using FETK.

Michael HolstUniversity of California, San DiegoUSAmholst@cam.ucsd.edu

CS07 Abstracts 157

MS107

A fully Implicit Adaptive Multigrid Scheme for theSolution of Nonlinear Time-Dependent PDEs Aris-ing in Phase-Field Models of Rapid Solidification

One of the most powerful techniques for modelling den-dritic micro structures is the Phase Field method. Theresulting governing equations are highly nonlinear time-dependent PDEs which we solve using adaptivity in bothspace and time. The temporal error control requires a fullyimplicit integration scheme to overcome stability restric-tions: the resulting nonlinear algebraic equations at eachtime step are solved using a composite multigrid scheme.The method will be demonstrated for both pure metal andbinary alloy solidification.

Peter JimackUniversity of Leeds, UKpkj@comp.leeds.ac.uk

Jan Rosam, Andrew MullisUniversity of Leedsrosam@comp.leeds.ac.uk, a.m.mullis@leeds.ac.uk

MS108

Accelerating Scientific Exploration with WorkflowAutomation Systems

The increasing complexity of modern scientific investiga-tions - a series of structured activities and computationsthat arise in scientific problem-solving, requires an inte-grated network-based support framework that allows scien-tists to reduce information technology overhead and focuson scientific research and discovery. This presentation dis-cusses long-term practical experiences of the U.S. Depart-ment of Energy Scientific Data Management Center withautomation of large scientific workflows. We will describethe current status and usage of a scientific workflow sys-tem, called Kepler, to automate the scientific explorationprocess.

Scott KlaskyORNLtba@ornl.gov

Ilkay AltintasSan Diego Supercomputer Centeraltintas@sdsc.edu

Terence CritchlowLLNLcritchlow@llnl.gov

Bertram LudaescherUCDavisludaescher@cs.ucdavis.edu

Steve ParkerUniversity of Utahsparker@cs.utah.edu

Mladen VoukNCSUvouk@ncsu.edu

MS108

High-Performance Parallel Data and Storage Man-

agement

Parallel data access support for computational science hasevolved into a sophisticated set of layered components de-signed to attain high performance and to provide conve-nient abstractions for data access. In this talk we will dis-cuss the architecture of these ”I/O software stacks”. We’llstart by describing the challenges in providing effectivedata access to computation science applications, and thenwe will discuss how the components in the I/O softwarestack work together to meet these challenges, citing exam-ples from real applications. We’ll conclude by discussingareas that researchers are exploring in order to enable ap-plications to make even better use of data storage systemson high-end machines.

Alok ChoudharyNorthwestern Universitytba

Rob RossArgonne National Laboratorytba

MS108

Mining Science Data

The data from scientific simulations, observations, and ex-periments is now being measured in terabytes and will soonreach the petabyte regime. The size of the data and itscomplexity make it difficult to find useful information inthe data. This is disconcerting to scientists who wonderabout the science still undiscovered in the data. The Sap-phire project (http://www.llnl.gov/casc/sapphire) is ad-dressing this concern by applying data mining techniquesto problems ranging in size from a few megabytes to ahundred terabytes. Using examples from fluid mixing, as-tronomy, remote sensing, and experimental physics, I willdiscuss our experiences in mining science data.

Chandrika KamathLawrence Livermore National Laboratorytba

MS108

High Performance Statistical Computing with Par-allel R and Star-P

Tera- and peta-scale scientific data sets generated by con-temporary simulations or high-throughput experimentsbring new challenges to existing environments for statis-tical computing. New paradigms for ultrascale data an-alytics are emerging to address these challenges. ParallelR aims to provide efficient parallel statistical computingenvironment that: (a) automatically detects and executestask-parallel analyses in sequential R codes; (b) allows toeasily plug-in data-parallel analyses codes in MPI-basedC/C++/Fortran. Star-P exploits a similar paradigm formultiple languages: MatLab, Mathematica, Python, etc.We will present under-the-hood implementation intricaciesof both systems, and demonstrate their usage by scientificapplications in biology, climate, and nanoscience.

Alan EdelmanDepartment of MathematicsMassachusetts Institute of Technologyedelman@mit.edu

Nagiza F. Samatova

158 CS07 Abstracts

Oak Ridge National LaboratoryComputer Science & Mathematics Divisionsamatovan@ornl.gov

PP0

Computer Simulation and Rheological Study ofXanthan Gum

Xanthan gum is a natural polysaccharide used as a foodadditive and rheological modifier. It is produced by thebacterium Xanthomonas campestris. Viscosity and elas-ticity properties of xanthan gum were studied for variouspH using AR2000 rheometer with cone and plate geom-etry. The temperature and frequency dependence of lossand storage modules were also studied and data were fit-ted with well known model. Same experimental data wereused to do computer simulation. In computer simulation,we designed the same geometry and used the experimentaldata to compare with the simulation data.

Leela RakeshCentral Michigan UniversityApplied Mathematics GroupLRakesh@aol.com

Stanley Hirschi, Ekmagage Almeida, Anja MuellerCentral Michigan Universityhirsc1s@cmich.edu, almei1ed@cmich.edu,muell1a@cmich.edu

PP0

A Hybrid Optimization Approach for the OptimalDesign of Traveling Wave Tubes

We will present a hybrid optimization approach for the op-timal design of electron device based on two independentphysics-based design and simulation codes. In particular,we use the CHRISTINE suite of large signal codes to modelthe slow wave circuit, in conjunction with Beam OpticsAnalysis to model a multi-stage depressed collector. Thesetwo simulation codes will be combined in a hybrid frame-work to automate the process of optimizing several phys-ical parameters while realizing several design constraints.The equations describing the device properties as well asthe objective functions will be discussed, and examples ofoptimized TWTs will be presented.

Adam AttarianNC State Universityarattari@unity.ncsu.edu

R. Lawrence IvesCalabazas Creek Research, Inc.rli@calcreek.com

John David, Hien TranCenter for Research in Scientific ComputationNorth Carolina State Universityjadavid2@ncsu.edu, tran@ncsu.edu

PP0

Computational Theory Using Gene RegulatoryNetwork

Complex networks found in biological beings are in factmysterious. Mimicking the networks has been practiced inmany types of mathematical models. Boolean networks,Petri nets, Bayesian networks, graphical Gaussian models,

Stochastic Process Calculi are examples of this imitation.Within this presentation, we introduce another approachto biology imitation. Using the gene regulatory networkwe develop a generic model, which we suspect useful forengineering computation.

Ahmad Yusairi Bani HashimKolej Universiti Teknikal Kebangsaan Malaysiayusairi@kutkm.edu.my

PP0

Implementing Machine Learning for Solver Selec-tion

Machine learning techniques have proven to be effective inselecting efficient solvers for linear systems. Linear systemsare represented by a set of matrix properties and appli-cation parameters combined into ”feature-vectors”. Thisposter highlights some factors that affect the accuracy ofsolver selection. We present a comparison of two classifica-tion methods, Boosting and Support Vector Machines. Wealso discuss the process of generating feature-vectors andthe optimal composition of their element set.

Sanjukta BhowmickColumbia Universitybhowmick@mcs.anl.gov

Erika FuentesUniversity of Tennesseeefuentes@cs.utk.edu

Yoav FreundDepartment of Computer Science and Engineering,University of California, San Diegoyfreund@ucsd.edu

David E. KeyesColumbia UniversityDepartment of Applied Physics & Applied Mathematicsdavid.keyes@columbia.edu

Victor EijkhoutThe University of Texas at AustinTexas Advanced Computing Centereijkhout@tacc.utexas.edu

PP0

Accurate Model Selection Computations

I will discuss a model selection methodology which includesmodels for deterministic individual dynamics and randompopulation effects in the context of HIV infection dynamics.Preliminary results concerning the numerics of the inverseproblem and the realistic distinguishability of a class ofmodels will be presented. In particular, I will focus on therelationship between random sources of error and thosearising from the numerical discretization.

David M. BortzUniversity of ColoradoDepartment of Applied Mathematicsdmbortz@colorado.edu

PP0

Application of URVD Updating Techniques to the

CS07 Abstracts 159

Template Tracking Problem

Template tracking is a well studied problem in computervision which refers to tracking an object through a videosequence by extracting an image of the ob ject (template)from the first frame and using it to find the regions in theremaining frames that correspond, as closely as possible,to the template. This framework has been extended by al-lowing parametric deformations of the template and linearappearance variations. One of the challenges in templatetracking is how to update the template so that it remainsa good model of the ob ject being tracked. A solution pro-posed recently by Matthews et al. (2003) is to update thetemplate and the appearance variation parameters at ev-ery iteration. Since this matrix changes every time a newframe arrives, these updates involve calculation of the prin-cipal components of the augmented image matrix at everyiteration. Traditionally, the principal components are com-puted at every iteration; we suggest algorithms to updatethe principal components obviating the need to recomputethem from scratch at every iteration.

Jesse L. BarlowPenn State UniversityDept of Computer Science & Engbarlow@cse.psu.edu

Anupama ChandrasekharPennsylvania State Universityachandra@cse.psu.edu

PP0

Relating Mesh Quality Metrics to Sparse LinearSolver Performance

Large scale computational modeling and simulation in-volves unstructured finite difference or finite elementmeshes and solution of related sparse linear systems. Wenow attempt to relate well known mesh quality metricsto convergence characteristics of sparse krylov space linearsolvers. We analyze the behavior of these quality metricsfor a suite of different meshes and their perturbations andrelate them to the performance of the underlying sparsekrylov space solver.

Padma RaghavanThe Pennsylvania State Univ.Dept of Computer Science Engr.raghavan@cse.psu.edu

Suzanne M. ShontzDepartment of Computer Science and EngineeringThe Pennsylvania State Universityshontz@cse.psu.edu

Anirban ChatterjeePennsylvania State Universityachatter@cse.psu.edu

PP0

Hyperspectral Imaging

A hyperspectral image typically has more than 200 spectralbands that can include not only the visible spectrum, butalso the infrared and ultraviolet spectra as well. The extrainformation in the spectral bands can be used to classifyobjects in an image with greater accuracy. Due to the highinformation content of a hyperspectral image and redun-dancy in the data, dimension reduction is an integral part

of analyzing a hyperspectral image.

Andrea L. BertozziUCLA Department of Mathematicsbertozzi@math.ucla.edu

Alex Chen, Meiching Fong, Zhong HuUniversity of California, Los Angelesachen@math.ucla.edu, meifong@ucla.edu,zhongwenhu@yahoo.com

PP0

Stability and Scalability of 2D Swarming Patterns

A swarming system is used to describe the aggregation ofanimals in biology and autonomous vehicles in engineering.We observe various distinct states with a dynamic modelby changing its parameters. While these patterns exhibitdifferent scalability properties, we apply H-stability fromstatistical mechanics to investigate such a difference. Tofurther analyze the system, a continuum description is de-rived from the discrete model. Its validity is tested and alinear stability analysis is given.

Yao-li ChuangDuke UniversityTBA

Maria D’OrsognaUniversity of California, Los Angelesdorsogna@math.university of california, los angele

Daniel MarthalerNorthrop Grumman Corp.daniel.marthaler@ngc.com

Andrea Bertozzi, Lincoln ChayesUniversity of California, Los Angelesbertozzi@math.university of california, los angele, tba

PP0

Strong Stability Preserving Multirate Schemes forHyperbolic Conservation Laws

This work will consider the problem of designing 3-D elec-tron guns using computer optimization techniques. Sev-eral different design parameters related to gun geometryand physical properties will be manipulated while consid-ering multiple design criteria related to beam properties.The equations modeling the electron beam dynamics andthe optimization routines will be described. Finally, exam-ples of guns designed using these techniques will also bepresented.

Emil M. ConstantinescuVirginia Polytechnic Institute and State Universityemconsta@cs.vt.edu

Adrian SanduVirginia Polytechnic Instituteand State Universityasandu@cs.vt.edu

PP0

A Parallel Lagrangian-Eulerian Coupling Algo-rithm for the Simulation of Floating Bodies in In-

160 CS07 Abstracts

compressible 2-Phase Flows

This poster concerns the parallel and accurate simulationof floating rigid bodies in incompressible two-phase flows.The coupling between the fluid and the solid response willbe achieved with an Eulerian-Lagrangian coupling algo-rithm based on the Level-Set method. The underlyingconservation laws at the interface are enforced by applyingproper interface boundary conditions to the fluid which ad-ditionally have to prevent geometrically inadmissible pen-etrations.

Michael Griebel, Roberto CroceUniversity of Bonn, Germanygriebel@ins.uni-bonn.de, croce@ins.uni-bonn.de

PP0

The Variational Brain

The Center for Computational Biology at UCLA has beendeveloping computational methods to help understand-ing quantitatively the brain. For example, we investigatemethods to detect morphological variations of brain struc-tures as empirical evidences have suggested that shape andsize play an important role in the assessment of the brainin health and disease. We will present a collection of vari-ational energy minimization approaches and their resultssupporting the Center’s mission. These include corticalsurface segmentation with multiple level sets, brain im-age registration using large deformation log-unbiased fluidmodels, direct mapping of cortical and hippocampal sur-faces with landmark constraints, and total variation basedfiltering and feature detection, modeling, and registrationof brain images.

Luminita A. VeseUniversity of California, Los AngelesDepartment of Mathematicslvese@math.ucla.edu

Paul M. ThompsonDepartment of NeurologyUCLA School of Medicinethompson@loni.ucla.edu

Jason ChungUniversity of California, Los AngelesDepartment of Mathematicssenninha@math.ucla.edu

Alexandre CunhaCenter for Computational BiologyUniversity of California, Los Angelescunha@ucla.edu

Yonggang Shi, Alex Leow, Ivo Dinov, Igor YanovskyUniversity of California, Los Angelesyonggang.shi@loni.ucla.edu, aleow@loni.ucla.edu,dinov@loni.ucla.edu, yanovsky@math.ucla.edu

Arthur TogaUCLALaboratory of Neuro Imagingtoga@loni.ucla.edu

PP0

Electron Gun Design Using Computer Optimiza-

tion

This work will consider the problem of designing 3-D elec-tron guns using computer optimization techniques. Sev-eral different design parameters related to gun geometryand physical properties will be manipulated while consid-ering multiple design criteria related to beam properties.The equations modeling the electron beam dynamics andthe optimization routines will be described. Finally, exam-ples of guns designed using these techniques will also bepresented.

R. Lawrence Ives, Thuc BuiCalabazas Creek Research, Inc.rli@calcreek.com, bui@calcreek.com

John David, Hien TranCenter for Research in Scientific ComputationNorth Carolina State Universityjadavid2@ncsu.edu, tran@ncsu.edu

PP0

Adaptive Global Surrogate Modeling

Due to the scale and computational complexity of currentsimulation codes, metamodels (or surrogate models) havebecome indispensable tools for exploring and understand-ing the design space. Consequently, there is great inter-est in techniques that aid the construction and evalua-tion of such models while minimizing the computationalcost and maximizing metamodel accuracy. We present anovel, adaptive, integrated approach to global metamodel-ing based on the Multivariate Metamodeling Toolbox (M3-Toolbox).

Tom B. DhaeneUniversity of Antwerptom.dhaene@ua.ac.be

Karel Crombecq, Cvan AarleUniversity of Antwerp, Belgiumkarel.crombecq@ua.ac.be, wim.vanaarle@ua.ac.be

Dirk Gorissen, Wouter HendrickxUniversity of Antwerpdirk.gorissen@ua.ac.be, wouter.hendrickx@ua.ac.be

PP0

Fully Implicit Solutions for Reduced Magnetohy-drodynamics Models

We describe fully implicit solutions for one- and two-fluid,reduced, time dependent, magnetohydrodynamics models.Our approach uses Newton-Krylov-Schwarz techniques andis second order accurate in space and up to fourth orderaccurate in time. The advantage of implicit solutions overtheir explicit counterparts follows from the larger implicittime step sizes, constrained only by accuracy requirementsand not by stability requirements as in the explicit case.We illustrate this by comparisons with explicit solutions,reporting computational results obtained on a parallel plat-form using thousands of processors.

Xiao-Chuan CaiUniversity of Colorado, BoulderDept. of Computer Sciencecai@cs.colorado.edu

Florin Dobrian

CS07 Abstracts 161

Columbia Universitydobrian@cs.odu.edu

David KeyesColumbia UniversityBrookhaven National Laboratorykd2112@columbia.edu

Serguei OvtchinnikovUniversity of Colorado at BoulderDepartment of Computer Scienceserguei.ovtchinnikov@colorado.edu

PP0

A Numerical Algorithm for MHD of Free SurfaceFlows at Low Magnetic Reynolds Numbers

We present a numerical algorithm which uses front track-ing and embedded boundary method for the study of themagnetohydrodynamics (MHD) of free surface flows at lowmagnetic Reynolds numbers. The code has been validatedthrough the numerical simulations of a liquid metal jet en-tering a non-uniform magnetic field and is currently beingused for the simulation of liquid targets for future accel-erators and pellet fueling of thermonuclear reactors (toka-maks).

James G. GlimmSUNY at Stony BrookDept of Applied Mathematicsglimm@ams.sunysb.edu

Roman SamulyakBrookhaven National Laboratoryrosamu@bnl.gov

Jian DuStony Brook Universityjidu@ams.sunysb.edu

Zhiliang XuBrookhaven National LabSUNY Stony Brookxuzhi@bnl.gov

PP0

Multigrid Preconditioning for One-Shot Newton-Krylov Methods in PDE-Constrained Optimization

We present a multigrid one shot method for the solutionof PDE-constrained optimization problems. Linearizationof the coupled nonlinear optimality system is done with aninexact Newton method, the resulting linear systems aresolved with a Krylov method. Since the arising KKT-typesystems are indefinite and ill-conditioned, effective precon-ditioning is mandatory for their efficient solution. As pre-conditioner we use parallel multigrid with smoother andcoarse grid solver adapted to optimal control problems.

Martin Engel, Michael GriebelUniversity of Bonn, Germanyengel@ins.uni-bonn.de, griebel@ins.uni-bonn.de

PP0

Meshless Formulations of PDEs Governing Electro-

magnetic Transients

In this paper an advanced meshless particle method forelectromagnetic transient analysis is presented. The aim isto obtain numerical solutions for electromagnetic problemsby avoiding the mesh generation and by employing a setof particles arbitrarily placed in the problem domain. Themeshless Smoothed Particle Hydrodynamics method hasbeen reformulated for solving the time domain Maxwellscurl equations. Test problems, dealing with even and un-even particles distribution, are simulated to validate theproposed methodology.

Elisa FrancomanoDipartimento di Ingegneria InformaticaUniversita degli Studi di Palermo - Italiae.francomano@unipa.it

Adele Tortorici, Elena Toscano, Guido AlaUniversita degli Studi di Palermoa.tortorici@unipa.it, etoscano@unipa.it,ala@diepa.unipa.it

PP0

A New Theory Extending Continuum Mechanicsto the Nanoscale and Applications

We present a new theory extending continuum mechan-ics to the nanoscale. While several successful applicationshave been developed, we will focus on one one which illus-trates the theory by studying a nonlinear boundary valueproblem resulting from a novel approach to modeling frac-ture of a brittle material.

Kaibin FuTexas A&M Universitykaibin@tamu.edu

PP0

A Comparative Study of Preconditioned IterativeSparse Linear Solver Packages

This study evaluates a suite of preconditioners based on in-complete factorization, approximate inverse and algebraicmultilevel schemes available in packages such as PETSC,Trilinos, HYPRE, PARMS and WSMP. We compare theperformance of these preconditioners on a set of benchmarkproblems using the recommended set of parameters. Ourobservations provide insight into the strengths and weak-nesses of the preconditioners in each package. These resultscan be used to guide the selection of the best package.

Anshul GuptaIBM T J Watson Research Centeranshul@watson.ibm.com

Vivek SarinTexas A&M UniversityDepartment of Computer Sciencesarin@cs.tamu.edu

Thomas GeorgeTexas A&M Universitytgeorge@cs.tamu.edu

162 CS07 Abstracts

PP0

TSP on Multi-Digraphs

The problem is to find a lightest tour in a given weightedmulti-digraph. The tours can be presented with circularpermutation matrices. The matrices are vectors in the vec-tor space of square matrices. Decomposition of tours overthe spaces basis reduces the problem to a non-symmetricalLP problem.

Sergey GubinGenesys Telecommunication Laboratoriessgubin@genesyslab.com

PP0

Combined Parareal/reduced Order ModelingMethod for Time-dependent PDEs

Due to the computational intensity of solving nonlinearpartial differential equations, there has been much inter-est in developing algorithms which improve the ability toperform real-time calculations. One approach to reducingcomputational costs is the development of low-dimensionalmodels; a second approach is to distribute the work overmultiple processes by the development of parallel algo-rithms. In this work we combine both approaches by usingPOD based reduced order modeling in space and a parallel-in-time algorithm for the temporal integration known asthe parareal algorithm.

Chris HardenFlorida State Universitycharden@scs.fsu.edu

Janet PetersonSchool of Computational Science,Florida State Universitypeterson@csit.fsu.edu

PP0

PDE-Based Parameter Reconstruction Through aParallel Newton-Krylov Method

We consider distributed parameter identification problemsfor the FitzHugh-Nagumo system that models the propa-gation of transmembrane electrical potentials in excitablemedia such as neurons or heart tissues. We have developeda parallel algorithm of Newton-Krylov type for such an in-verse problem. The method combines Newtons method fornumerical optimization with Krylov subspace solvers forthe reduced KKT system. We show by numerical simula-tions that the excitation parameter can be recovered fromboundary measurements.

David KeyesColumbia UniversityBrookhaven National Laboratorykd2112@columbia.edu

Yuan HeColumbia Universityyh2030@columbia.edu

PP0

Combinatorial Algorithms Enabling Computa-tional Science

Combinatorial Scientific Computing is concerned with the

development, analysis and utilization of discrete algorithmsin scientific and engineering applications. Graph and ge-ometric algorithms are the fundamental tools of combina-torial scientific computing. They play a crucial enablingrole in numerous areas, including sparse matrix compu-tation, partitioning for parallelization, mesh generation,and automatic differentiation. In this poster we report onsome recent developments in this highly interdisciplinaryand rapidly evolving field.

Alex PothenOld Dominion UniversityDept of Computer Sciencepothen@cs.odu.edu

Erik G. BomanSandia National Labs, NMDiscrete Math and Algorithmsegboman@sandia.gov

Karen D. DevineSandia National Laboratorieskddevin@sandia.gov

Paul D. HovlandArgonne National LaboratoryMCS Division, 221/C236hovland@mcs.anl.gov

Todd S. MunsonArgonne National LaboratoryMathematics and Computer Science Divisiontmunson@mcs.anl.gov

Bruce HendricksonSandia National Labsbahendr@sandia.gov

Sanjukta BhowmickDepartment of Applied Physics and Applied MathematicsColumbia Universitybhowmick@cse.psu.edu

Umit CatalyurekOhio State Universitycatalyurek.1@osu.edu

Assefaw H. GebremedhinComputer Science DepartmentOld Dominion Universityassefaw@cs.odu.edu

PP0

Using Supervised Machine Learning Techniques toPredict Preconditioner Behavior

Choosing the right preconditioner is a critical componentof using iterative methods to solve Ax = b for large, sparseA. However, given a specific matrix A, few guidelines existfor choosing a preconditioner and setting its parameters ef-fectively. With the goal of providing useful guidelines, weexplore the use of supervised machine learning techniques,such as neural networks, for predicting the behavior of pre-conditioned iterative methods.

Tzu-Yi ChenPomona Collegetzuyi@cs.pomona.edu

CS07 Abstracts 163

America HollowayComputer Science DepartmentPomona Collegeamerica.holloway@pomona.edu

PP0

A Model for Timely Decision as a CompetitiveEdge

Making timely decisions is considered to be a major factoras a competitive edge in the business world. To quantifythis factor, we consider a model with two competitive busi-nesses that differ in the delay time of making and imple-menting decisions. A time-delayed dynamic system is usedto simulate the effect of delays in decisions. Results showthat business with shorter decision delays experiences lessfluctuation and is more adaptive to the changing businessenvironment.

Jiashi HouNorfolk State Universityjhou@nsu.edu

PP0

Long Time Behavior of Numerical Solutions forProblems with Coarsening

We use the Cahn-Hilliard equation as a model of coars-ening systems to study its long time behavior under theinfluence of discretization errors. In particular, we investi-gate the scaling properties of discretization errors to guidethe design of a gradient stable time stepping method, theultimate goal being to compute the slow dynamics both effi-ciently and accurately. The solution procedure and resultsfrom various time stepping approaches will be presented.

Andrea L. BertozziUCLA Department of Mathematicsbertozzi@math.ucla.edu

Shao-Ching Huang, Shibin DaiUniversity of California, Los Angelesschuang@ats.ucla.edu, sdai@math.ucla.edu

PP0

Nonlinear Dynamical Analysis of Multi-ChannelNeonate EEG Time Series During Sleep

Nonlinear dynamical analysis of the EEG time series dur-ing sleep is used to investigate the dynamics of neurode-velopment. As an alternative to reconstructing the statevector using time-delay embedding a single-channel of therecorded EEG time series, a 14 individual channels mea-suring electrical activity from different regions of the brainis used for the computation of correlation dimension. Brainactivity as quantified by correlation dimension provides agood indicator of neurodevelopment.

Suparerk Janjarasjitt, Mark Scher, Kenneth LoparoCase Western Reserve Universitysuparerk.janjarasjitt@case.edu, mark.scher@case.edu, ken-neth.loparo@case.edu

PP0

Cooperative Boundary Tracking with EmbeddedNonlinear Filter

In this work, we consider the problem that using multi-

ple autonomous underwater vehicles (AUVs) to track envi-ronmental boundaries. Assuming each AUV has a simpledensity detector, we demonstrate that, with our bound-ary estimation and motion control algorithms, AUVs trackthe boundary efficiently. Also, embedded nonlinear filtersgreatly improve the reliability against sensor noise. More-over, a cooperative scheme is proposed so that multipleAUVs can track and estimate the boundary optimally us-ing limited communication bandwidth.

Andrea L. BertozziUCLA Department of Mathematicsbertozzi@math.ucla.edu

Zhipu JinUniversity of California, Los Angeleszhipu@math.ucla.edu

PP0

Modeling of Contaminant Transport in Groundwa-ter Via Exact Simulation of Diffusions

It is well known that a advection-dispersion equation(ADE) can be interpreted as forward-Kolmogorov equa-tion, also called Fokker-Planck equation, of a diffusionprocess given by a stochastic differential equation. Suchsolute transport can be simulated by generating pathsof this process. We use a new method (A. Beskos andG.O. Roberts, Exact simulation of diffusions, The Annalsof Applied Probability 2005, vol. 15(4), 2422-2444) to ob-tain a ’particle solution’ of the ADE. We compare the re-sults with those obtained by the forward reverse methodof Milstein et al. (Bernoulli 2004, vol. 10(2), 281- 312)for transition density estimation. Furthermore we adresssensivity analysis of exceedance probabilities with respectto variations of the transmissivity field, porosity and dis-persivity.

Franz KonecnyBOKU-University of Natural Resources and AppliedLife Sciences, Viennafranz.konecny@boku.ac.at

PP0

An Efficient Direct Parallel Elliptic Solver by theSpectral Element Method

An efficient direct elliptic solver based on the spectral ele-ment discretization is developed. The direct solver is basedon a matrix decomposition approach which reduces multi-dimensional problems to a sequence of one-dimensionalproblems that can be efficiently handled by a static con-densation process. Thanks to the spectral accuracy andthe localized nature of a spectral element discretization,this elliptic solver is of spectrally accurate and can be effi-ciently parallelized.

Jie ShenDepartment of MathematicsPurdue Universityshen@math.purdue.edu

Yuen Yick KwanPurdue Universityykwan@math.purdue.edu

164 CS07 Abstracts

PP0

Benchmarking OpenMPI

OpenMPI, the successor to LA-MPI, FT-MPI, LAM/MPI,and PACX-MPI, offers significant improvements over thecurrent implementations. These include fault tolerant net-working and check-point/restart capabilities. The need forthese features will increase as demand for petascale com-puting grows. While development continues on OpenMPI,it is important to maintain and improve work from pre-vious MPI implementations on optimization of bandwidthand latency for network transfers. We compare OpenMPIto other implementations at the network and applicationlevel.

Charlie PeckEarlham Collegecharliep@cs.earlham.edu

Alex Lemann, Kevin HunterCluster Computing GroupEarlham Collegelemanal@cs.earlham.edu, kevin@cs.earlham.edu

PP0

Microfluidics of an Electrowetting Drop

We propose a diffuse interface model for drop motion, dueto electrowetting, in a Hele-Shaw geometry. In the limit ofsmall interface thickness, asymptotic analysis shows themodel is equivalent to Hele-Shaw flow with a voltage-modified Young-Laplace boundary condition. The detailsof the contact angle significantly affect the timescale of mo-tion in the model. The shape dynamics in the model agreewell with the experiment, down to the length scale of thediffuse interface thickness.

Andrea L. BertozziUCLA Department of Mathematicsbertozzi@math.ucla.edu

Karl GlasnerThe University of ArizonaDepartment of Mathematicskglasner@math.arizona.edu

Hsiang-Wei Lu, Chang-Jin KimUniversity of California, Los Angeleshwlu@University of California, Los Angeles.edu,cjkim@university of california, los angeles.edu

PP0

Phase-Aware Hardware Adaptivity for Energy-Aware High Performance Computing

For large multiprocessor installations improving the ther-mal and energy efficiency of scientific workloads is becom-ing increasingly critical. We conjecture that scientific codesconsist of distinct phases. We therefore propose runtimephase detection schemes for adaptive hardware selectionto improve energy efficiency. Our preliminary results indi-cate that by adaptively selecting power aware caches, CPUgears, data prefetchers and a load miss predictor, we canachieve power reduction of 14%, energy reduction of 43%while reducing the execution time by 32%.

Padma RaghavanThe Pennsylvania State Univ.Dept of Computer Science Engr.

raghavan@cse.psu.edu

Mary Jane IrwinCompter Science & EngineerinPennsylvania State Universitymji@cse.psu.edu

Konrad MalkowskiPenn State UniversityUSAmalkowsk@cse.psu.edu

PP0

General Approach for the Numerical Solution ofInverse Problems

We need to use some sort of regularization techniques forthe numerical solution of inverse problems. Especially forthe cases where some features of the solution exhibit dif-ferent patterns, along its different subspaces , the usualfixed regularization techniques can not compute a satisfac-tory solution. In this work, we develop an algorithm foradaptive regularization techniques based on the concept ofTikhonov regularization method. The basic idea is to usemultiple regularization parameters.

Kourosh ModarresiStanford UniversitySCCMkourosh.modarresi@stanford.edu

PP0

Verification Tests for Computational, Multigroup,Radiation Hydrodynamics in Two Spatial Dimen-sions

We have developed a computationalradiation-hydrodynamics algorithm, in two spatial dimen-sions, designed to model astrophysical problems in stellar-core collapse, shock propagation, and proto-neutron-starevolution. Accurate modeling of such phenomena requiresa rigorous verification process. We present here a test suitedesigned to stress diverse aspects of our code by compar-ing its output to known analytic solutions. It includes testsof pure hydrodynamics, pure radiation, and problems thatcouple these components together.

F. Douglas Swesty, Eric MyraState University of New York at Stony Brookdswesty@mail.astro.sunysb.edu,emyra@mail.astro.sunysb.edu

PP0

Large-Scale Coupled Simulations for Seismic Re-sponse of Multiple Oil-Storage Tanks

This work is a part of gIntegrated Predictive SimulationSystem for Earthquake and Tsunami Disasterh, a 5-yearproject from FY.2005, supported by Japanese Government.In this poster, frameworks, such as data structure, and ap-plication interface, for large-scale parallel coupling simula-tions for seismic response of multiple tanks for oil-storagewith fluid-structure interaction using finite-element meth-ods are described. Preliminary results of coupled simu-lations on PC cluster with 64 corefs will be also demon-strated.

Takashi Furumura

CS07 Abstracts 165

Earthquake Research InstituteUniversity of Tokyofurumura@eri.u-tokyo.ac.jp

Hiroshi OkudaRACE, University of Tokyookuda@race.u-tokyo.ac.jp

Toshio NagashimaSophia Universitynagashim@me.sophia.ac.jp

Tsuyoshi IchimuraTIT/JST, Japanichimura@cv.titech.ac.jp

Kengo NakajimaThe University of TokyoDepartment of Earth & Planetary Sciencenakajima@eps.s.u-tokyo.ac.jp

Masaaki MatsumotoMitsubishi Research Institute, Inc.matsumot@mri.co.jp

PP0

BCCD/LittleFe - Computational Science Educa-tion on the Move

One of the principle challenges to computational science,high performance computing, and Grid education is thatmany institutions do not have access to appropriate plat-forms for demonstrations and laboratories. LittleFe is aninexpensive design for a 4-8 node portable computationalcluster. LittleFe uses the Bootable Cluster CD (BCCD),a standard Linux environment with a complete set of par-allel and distributed computing tools. LittleFe is an in-expensive, easy to use solution for computational scienceeducation.

Alex LemannCluster Computing GroupEarlham Collegelemanal@cs.earlham.edu

Charles PeckCluster Computing Group, Computer ScienceEarlham Collegecharliep@cs.earlham.edu

Kevin HunterCluster Computing GroupEarlham Collegekevin@cs.earlham.edu

David A. JoinerKean UniversityAssistant Professordjoiner@kean.edu

Paul GrayUniversity of Northern IowaComputer Sciencegray@cs.uni.edu

Thomas P. MurphyContra Costa CollegeComputer Science

tmurphy@contracosta.edu

PP0

DNA Micro-Array Optimization with Synthesisand Sequence Composition Constraints

DNA micro-array hybridization is a high-throughput tech-nology extensively used in genomic analysis. Recent ad-vances in high density microarray technology - increasedprobe density and specificity allow efficient probing oflarge eukaryote genomes. Whole genome probing howeverrequires efficient algorithms for oligonucleotide selectionand synthesis. We propose here local search algorithmsfor optimizing oligonucleotide selection with synthesis andsequence similarity constraints. The optimization methodwas used for designing high density isoTM tiling arrays.We discuss here the performance of proposed optimizationalgorithms.

George V. PopescuACMgeorge.popescu@acm.org

PP0

Implementation of Meshless Finite DifferenceMethod for Schrodinger Equation

Meshless methods have recently become popular for solvingvarieties of differential equations, with many applicationsin science and engineering fields. One of these methods,the meshless finite difference method, approximates a dif-ferential operator by using directional difference quotientsand their combinations. Here we present numerical resultsof implementing the meshless finite difference method forsolving Schrodinger equation.

Jeff RufinusWidener Universityrufinus@cs.widener.edu

PP0

Nonlinear Spectral Viscosity for the Navier-StokesEquations

Fluid turbulence in three dimension is a challenge both inanalysis and computation due to the need to resolve theeffects of small scales. In order to resolve this difficulty,various modeling strategies are employed. Ladyzhenskayaproposed the use of the nonlinear diffusion operator tomodel the small scale fluctuations. On the other hand, wemust also preserve the large-scale dynamics described bythe Navier-Stokes equations. Thus we use nonlinear dif-fusion in combination with spectral viscosity filter whichattempts to limit the nonlinear viscosity effects to highmodes. We analyze one such hybrid model, and prove ex-istence and regularity, as well as derive certain restrictionon the nonlinearity to preserve consistency with respect tothe Navier-Stokes equations. Thus we use nonlinear dif-fusion in combination with spectral viscosity filter whichattempts to limit the nonlinear viscosity effects to highmodes. We analyze one such hybrid model, and prove ex-istence and regularity, as well as derive certain restrictionon the nonlinearity to preserve consistency with respect tothe Navier-Stokes equations.

Yuki SakaSchool of Computational Science and InformationTechnologyFlorida State University

166 CS07 Abstracts

saka@csit.fsu.edu

PP0

The Double Globe Method: A Novel AdaptiveNeighborhood Controller for Meta-Heuristic Algo-rithms

In a meta-heuristic optimization algorithm, at each it-eration, a neighborhood is defined in which new solu-tions would be generated. We propose a novel adaptivescheme for controlling the stochastic search neighbour-hood. The proposed ”double globe” method features twohyper-spheres around the current optimum whose radii aredynamically enlarged or shrunk in order to adapt the de-gree of ”exploration” and ”exploitation.” Numerical exper-iments and further analysis demonstrate the effectivenessof the proposed scheme in conjunction with several meta-heuristic algorithms for combinatorial optimization prob-lems.

Behnam Sharif, Gaofeng Wang, Tarek ElMekkawyUniversity of Manitoba, Canadaumsharib@cc.umanitoba.ca, ggwang@me.umanitoba.ca,tmekkway@me.umanitoba.ca

PP0

Mode Pursuing Sampling Method for DiscreteVariable Optimization in Mechanical Design

Based on the previously developed Mode Pursuing Sam-pling (MPS) method for continuous variables, a variationfor discrete variable global optimization problems is de-vised. The proposed discrete-MPS method controls theconvergence behavior by dynamically resizing two hyper-spheres centered at the current optimum. The radii ofthe spheres adapt the extent of exploration and exploita-tion. Application of the proposed method to two chal-lenging mechanical design problems, namely pressure ves-sel and gear train, shows promising results compared toother commonly used algorithms

Behnam Sharif, Gaofeng Wang, Tarek ElMekkawyUniversity of Manitoba, Canadaumsharib@cc.umanitoba.ca, ggwang@me.umanitoba.ca,tmekkway@me.umanitoba.ca

PP0

Parallel Hydrodynamic Simulations Using NewGeneration of the Multicore Processors

Multi-core revolution in the processor designs allows shift-ing the parallel hydrodynamic simulations from the dis-tributed CPU farms to a server or even a laptop whilemaintaining similar performance characteristics. The com-bination of the compact size, low cost, and energy con-sumption of a typical server with the power of a distributedparallel cluster gives the new generation of the multi-coreplatforms a potential to redefine the way hydrodynamicsimulations for oil and gas reservoirs are run. Since calcu-lations used in modeling require intensive CPU and mem-ory usage, one needs to verify that the multi-core hardwarearchitecture is efficient for this kind of calculations, on onehand, and that the software performance scales well withthe number of the available cores, on the other hand. Withfour cores of two Intels Woodcrest processors used in Bens-ley server, the simulation acceleration achieved on a num-ber of real full-field models exceeded factor of 3. Results

for Tulsa server platform are also discussed.

Vasilii ShelkovRock Flow Dynamics LLCvshelk@yahoo.com

Kirill BogachevLomonosov Moscow State Universitykirill.bogachev@gmail.com

PP0

Using Adaptive Proper Orthogonal Decompositionto Model Reacting Flow

We develop an adaptive proper orthogonal decomposition(aPOD) method to simulate reacting flow with detailedchemical kinetics. The scheme is based on the method ofsnapshots and uses different POD basis vectors in differ-ent regions of the computational domain. We demonstratethe use of aPOD on an unsteady one-dimensional reaction-diffusion model equation corresponding to a laminar pre-mixed methane-air flame. The observed speed-up factor isapproximately 3.5.

William H. GreenMIT Chemical Engineeringwhgreen@mit.edu

Michael SingerMassachusetts Institute of Technologymsinger@mit.edu

PP0

A Gradient-Based EM Algorithm for Maximizingthe Likelihood Function of an ARMA Process

The maximum likelihood estimate of an ARMA processcan be computed using a gradient-based EM algorithmcoupled with a reparameterization. Using the EM algo-rithm, an exact gradient can be computed while holdingthe predicted values at the current state fixed. The pre-dicted values are then updated in the expectation step.This approach avoids the use of a numerical approxima-tion to the gradient. Software demonstrating the approachwill be presented.

Jason StoverGeorgia College & State Universityjason.stover@gcsu.edu

PP0

Wavelet Lgorithm for High-Resolution Image Re-construction

Low-resolution samples of a scene, shifted by sub-pixellength, are used in an iterative process to obtain a high-resolution image. Obtaining a better approximation to thetrue image is modeled as a linear system Lf = g, where L isa blurring matrix, f is the true image and g is constructedfrom the low-resolution frames. This system is solved for fusing reconstruction and decomposition algorithms derivedfrom wavelet theory.

Samantha SummerUC Berkeleysamrose2006@gmail.com

Meghan Belinski

CS07 Abstracts 167

Loyola College in Marylandmebelinkski@loyola.edu

Andrea MartinezRegis Universitymarti844@regis.edu

PP0

Efficient and Load Balanced Force DecompositionAlgorithm for Parallel Molecular Dynamics Simu-lations

An algorithm, based on equal partitioning of the force ma-trix onto processors is presented. Asynchronous commu-nications efficiently hide communication between proces-sors. Communication is reduced by i) exchanging only non-redundant information between processors and ii) sortingparticles according to a space-filling Hilbert curve. Load-balancing is implemented by i) distributing equal numberof interactions on each processor or ii) balancing the timespent in the force routine. Results show good scaling be-havior especially for non-homogenous systems.

Florian JanoschekStuttgart University, Germanyf.j@noschek.de

Godehard SutmannResearch Centre Julich, Germanyg.sutmann@fz-juelich.de

PP0

A Parallel 2-Dimensional Wavelet Transformation

The 2-dimensional Wavelet transform T, formulated as aproduct of three matrices T = W tAW , is parallelized. Thesparsity of W is used explicitly to implement the algo-rithm as a double loop over an upper triangular matrix.Parallelization is performed by a scaled version of equalsub-areas of the triangular matrix, where processors workindependently on each sub-area. Scalability is shown, butnot limited, up to 128 processors.

Godehard SutmannResearch Centre Julich, Germanyg.sutmann@fz-juelich.de

PP0

Novel Computational and Statistical Approachesto Whole Genome Association Analysis

In human genetics, recent technological developments havecreated an explosion of whole genome single nucleotidepolymorphism (SNP) data and, consequently, substantialanalytical challenges. We describe an analysis toolset,PLINK, offering efficient implementations of existing meth-ods (basic association statistics, sample matching basedon inferred ancestry) as well as novel approaches includinga shared segment analysis using hidden Markov models.We describe the algorithms and their implementation inPLINK and also a user-friendly GUI, gPLINK.

K. E. O. Todd-BrownMassachusetts General Hospitalktoddbrown@pngu.mgh.harvard.edu

B. NealeKing’s College London, United Kingdom

b.neale@iop.kcl.ac.uk

M. J. DalyMassachusetts General Hospital and Broad Institutemjdaly@chgr.mgh.harvard.edu

P. C. ShamHong Kong University, Hong Kongpcsham@hkucc.hku.hk

S. M. PurcellMassachusetts General Hospital and Broad Instituteshaun@pngu.mgh.harvard.edu

PP0

Strongly Anisotropic Cahn-Hilliard Models

We compare different approaches for modeling stronglyanisotropic crystal and epitaxial growth using regularized,anisotropic Cahn-Hilliard-type equations. When the sur-face anisotropy is sufficiently strong, sharp corners formand unregularized anisotropic Cahn-Hilliard equations be-come ill-posed. Our models contain high order Will-more and linear regularizations to remove the ill-posedness.Then we provide matched asymptotic analysis to show theconvergence of the diffusive interface model to the usualsharp interface model. We also present 2D and 3D numer-ical results by adaptive finite-difference methods.

John LowengrubDepartment of MathematicsUniversity of California at Irvinelowengrb@math.uci.edu

Solmaz Torabi, Steve Wise, Shuwang LiUniversity of California, Irvinestorabi@uci.edu, swise@math.uci.edu, lis@math.uci.edu

PP0

Polarizability of Zeolitic Broensted Acidic Sites

The interacting induced-dipoles polarization model, imple-mented in POLAR, is used for calculation of effective polar-izability of zeolitic bridged OH group, which results muchhigher than that of the free silanol group. A high polar-izability is also calculated for the bridged OH group witha Si4+, in absence of Lewis-acid promotion of silanol byAl3+. Only when cations are located in the zeolite micro-pore, next to tetrahedra that contain trivalent cations, arelarge electrostatic fields generated.

Francisco TorrensUniversitad de Valencia, Spainfrancisco.torrens@uv.es

Gloria CastellanoUniversidad Politecnica de Valencia andUniversidad Catolica de Valencia San Vicente Martir,Spaingloria.castellano@yahoo.es

PP0

An Efficient Computational Tool ApproachingMultiscale Environments

In designing multiscale models process information are re-ported at multiple levels of resolution commonly involving

168 CS07 Abstracts

operations such as discrete convolution and upsampling. Inthis paper a non recursive computational tool which allowsto follow the evolution of a process across the scales by us-ing suitable vectors weight and involving only initial datasampling is provided. B-spline functions are well-knownin designing representation at different scales; experimentsinvolving centered cardinal B-spline functions are provided.

Elisa FrancomanoDipartimento di Ingegneria InformaticaUniversita degli Studi di Palermo - Italiae.francomano@unipa.it

Adele Tortorici, Elena ToscanoUniversita degli Studi di Palermoa.tortorici@unipa.it, etoscano@unipa.it

PP0

Performance Scalings of the Extended MHD NIM-ROD Code

The NIMROD code is a production-level code for solvingthe extended magnetohydrodynamic equations for fusionapplications and is part of the Center for Extended Magne-tohydrodynamic Modeling (CEMM) SciDAC. In this work,we will show results of studies aimed at understandingthe various factors influencing the parallel performanceof the time consuming matrix solves for production-levelproblems. We will especially focus on the performance ofthe SuperLU preconditioner, and the effectiveness of usingMETIS graph partitioning for the matrix reordering.

Xiaoye S. LiComputational Research DivisionLawrence Berkeley National Laboratoryxsli@lbl.gov

Srinath Vadlamani, Scott KrugerTech-X Corporationsrinath@txcorp.com, kruger@txcorp.com

Chris CareyUniv. of Wisconsin-Madisoncscarey@wisc.edu

Carl R. SovinecUniversity of Wisconsin-Madisonsovinec@engr.wisc.edu

PP0

Atomistic Psuedopotential Simulation of Nanome-ter Sized CMOS Devices

When the size of a CMOS is shrunk to 10-20 nm, quan-tum mechanical device simulation becomes necessary. Wehave developed a method to calculate the electronic struc-tures and I-V curves of million atom CMOS devices usingatomistic pseudopotentials. The electronic structure is de-scribed by an empirical pseudopotential, and the Hamil-tonian is diagonalized using a linear combination of bulkband algorithm. This approach is more accurate than thetraditional effective mass method.

Jun-Wei Luo, Shu-Shen Li, Jianbai XiaChinese Academy of Sciencesjwluo@red.semi.ac.cn, sslee@red.semi.ac.cn,xiajb@red.semi.ac.cn

Lin-Wang WangLawrence Berkeley National Lablwwang@lbl.gov

PP0

Model-Based Xampling for Bayesian Inverse Prob-lems

For large scale problems, the computational cost of evaluat-ing the forward model is one of the limiting factors of usingthe Bayesian approach for inverse problems. The standardmethods used to sample the posterior distribution gener-ally only use evaluations of the forward problem as inputinformation. We investigate using model-based informa-tion, (e.g., the Hessian of a misfit function), to reduce thecomputation cost of sampling the posterior distribution.

Omar Ghattas, Lucas WilcoxUniversity of Texas at Austinomar@ices.utexas.edu, lucasw@ices.utexas.edu

PP0

Components of a Hybrid Algorithm for StochasticCompressible Navier-Stokes

The Landau-Lifshitz Navier-Stokes (LLNS) equations usestochastic fluxes to describe fluctuating hydrodynamics.This poster examines explicit Eulerian discretizations ofLLNS; we find that the third-order Runge-Kutta integra-tor accurately produces density fluctuations while advanc-ing with large time steps. A variety of numerical testsare considered, comparing candidate stochastic LLNS PDEsolvers with theory and with molecular simulations. ThePDE solver and molecular simulation will be coupled toform a multiscale hybrid method.

John B. BellCCSELawrence Berkeley Laboratoryjbbell@lbl.gov

Alejandro GarciaLawrence Livermore National LaboratorySan Jose State Universityalgarcia@algarcia.org

Sarah A. WilliamsUC DavisGraduate Group in Applied Mathematicssawilliams@math.ucdavis.edu

PP0

Flux Surface-Following Discretization of MagneticReconnection

A dynamic flux surface-following solution-adaptive grid al-gorithm is proposed for the numerical simulation of themagnetic reconnection problem expressed by 2D resistiveHall magnetohydrodynamic equations. The transforma-tion is designed to capture solution features, especially thex-point and o-point structures of the reconnection with pre-cision, while reducing resolution requirements tangent tothe surfaces. The parallel, fully coupled, nonlinearly im-plicit Newton-Krylov-Schwarz algorithm is used to allow atime step based on accuracy and independent of stabilityconsiderations.

David Keyes

CS07 Abstracts 169

Columbia UniversityBrookhaven National Laboratorykd2112@columbia.edu

Rebecca YuanColumbia Universityxy2102@columbia.edu

PP0

Generalized Analytic Functions in 3D Axially Sym-metric Stokes Flows

A class of generalized analytic functions, defined by a spe-cial case of the Carleman system that arises in 3D asym-metric problems of hydrodynamics of Stokes flows, station-ary electromagnetic fields in conductive materials, etc., hasbeen considered. Hilbert formulas, establishing relation-ships between the real and imaginary parts of a general-ized analytic function from this class, have been derivedfor the domains exterior to the contour of spindle, lens,bi-spheres and torus in the meridional cross-section plane.This special case of the Carleman system has been reducedto a second-order difference equation with respect to eitherthe coefficients in series or densities in integral representa-tions of the real and imaginary parts. For spindle and lens,the equation has been solved in the framework of Riemannboundary-value problems in the class of meromorphic func-tions. For torus, the equation has been solved by meansof the Fourier transform, while for bi-spheres, it has beensolved by an algebraic method. As examples, analytical ex-pressions for the pressure in the problems of the 3D axiallysymmetric Stokes flows about rigid spindle-shaped body,lens-shaped body, bi-spheres and torus have been derivedbased on the corresponding Hilbert formulas.

Michael ZabarankinStevens Institute of Technologymzabaran@stevens.edu

PP0

Linear Scaling 3D Fragment Method for PetascaleNanoscience Simulations

O(N) methods are needed to solve large-scale nanoscienceproblems (with 1000-1000000 atoms) effectively, where Nis the number of atoms in the system. Unfortunately, mostof O(N) methods studied in the last decade have variousnumerical convergence problems and computer paralleliza-tion issues. We present a new O(N) method which hasan ab initio accuracy and scales linearly upto thousandsof processors. This approach provides a practical way forfuture petascale computation in materials/nanomaterialsscience.

Juan C. Meza, Zhengji ZhaoLawrence Berkeley National LaboratoryJCMeza@lbl.gov, zzhao@hpcrd.lbl.gov

Lin-Wang WangLawrence Berkeley National Lablwwang@lbl.gov

PP0

Runge-Kutta-Chebyshev Projection Method

We present a fully explicit, stabilized projection methodcalled the Runge-Kutta-Chebyshev (RKC) Projectionmethod for the solution of incompressible Navier-Stokes

systems. This method preserves the extended stabilityproperty of the RKC method for solving ODEs, and itrequires only one projection per step. An additional pro-jection on the time derivative of the velocity is performedwhenever a second order approximation for the pressure isdesired.

Linda R. PetzoldUniversity of California, Santa Barbarapetzold@engineering.ucsb.edu

Zheming ZhengUniversity of California Santa Barbarazhengzhm@engineering.ucsb.edu

PP0

Crystal Dissolution and Precipitation in PorousMedia

We consider a one-phase Stefan problem modelling a disso-lution and precipitation process in a porous medium. Themodel involves nonlinear and multi-valued exchange ratesat the free boundary. Analytic results are presented fora one dimensional setting and computational results forone and two dimensional settings. For the one dimensionalsimulations, a coordinate transform and a finite differencemethod is used. The two dimensional simulations use anArbitrary Lagrangian Eulerian method.

I. S. PopDept Mathematics and Computer ScienceEindhoven University of Technologyi.pop@tue.nl

T. L. van NoordenEindhoven University of Technologyt.l.v.noorden@tue.nl