experiences with large scale numerical simulation · 2015. 5. 13. · 1 experiences with large...
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Experiences withExperiences withLarge Scale Numerical Simulation Large Scale Numerical Simulation
Lehrstuhl für Informatik 10
(Systemsimulation)
www10.informatik.uni-erlangen.de
Dundee, June 28, 2005
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Ulrich Rüde
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OverviewOverview
MotivationThree examples
Material science and process technology:Metal FoamsNano TechnologyBiomedical Technology:The Inverse EEG problem
High End ComputingTrends in High End Numerical ComputingParallel Hierarchical Hybrid Grids (HHG) for FE simulationsParallel Lattice Boltzmann Methods for Free Surface Flow
Conclusions
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Part I
Motivation:Motivation:Computational ScienceComputational Science and Engineering (CSE) and Engineering (CSE)
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MotivationMotivation
“The panels overarching finding is that a new age has dawned in scientific and engineering
research …”
(from the “NSF report on Cyberinfrastructure”, Feb. 2003)
…. this revolution is driven by
Simulation for Technology and ScienceSimulation for Technology and Science
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PITAC Report to the US President on PITAC Report to the US President on
Computational ScienceComputational ScienceJune 2005June 2005
PRINCIPAL FINDING
Computational science is now indispensable to the solution of complex problems in every sector, from traditional science and engineering domains to such key areas as national security, public health, and economic innovation. Advances in computing and connectivity make it possible to develop computational models and capture and analyze unprecedented amounts of experimental and observational data to address problems previously deemed intractable or
beyond imagination.
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The Two Principles of ScienceThe Two Principles of Science
TheoryTheoryMathematical Mathematical Models, Differential Models, Differential Equations, NewtonEquations, Newton
ExperimentsExperimentsObservation and Observation and prototypesprototypes
empirical Sciencesempirical Sciences
Computational ScienceComputational Science
Simulation, OptimizationSimulation, Optimization
(quantitative) virtual Reality(quantitative) virtual Reality
ThreeThree
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ComputationalComputational ScienceScience and and EngineeringEngineering
ScienceScienceTechnologyTechnology
TheorTheoryy Observation Observation Experiment Experiment PrototypesPrototypes
ComputationComputationComputer SimulationComputer Simulation
VirtuVirtuaal l ExperimentsExperimentsVirtual PrototypesVirtual Prototypes
Virtual Virtual RealitRealityy
AlgorithmicAlgorithmic Modelling forModelling for PPhysihysicscs,, C Chemihemistry;stry;
Electrical Mechanical, Chemical Electrical Mechanical, Chemical Engineering; Material SciencesEngineering; Material Sciences
Bio- and Medical SciencesBio- and Medical Sciences,,……
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CSE is a broad CSE is a broad multidisciplinarymultidisciplinary area that encompasses area that encompasses applicationsapplications in science/engineering, applied mathematics, in science/engineering, applied mathematics, numerical analysis, and computer science. numerical analysis, and computer science. Computer models Computer models and computer simulationsand computer simulations have become an important part of the have become an important part of the research repertoire, supplementing (and in some cases research repertoire, supplementing (and in some cases replacing) experimentation. Going from application area to replacing) experimentation. Going from application area to computational resultscomputational results requires domain expertise, requires domain expertise, mathematical mathematical modeling, numerical analysis, algorithm development, software modeling, numerical analysis, algorithm development, software implementation, program execution, analysis, validation and implementation, program execution, analysis, validation and visualization of resultsvisualization of results. CSE involves all of this. CSE involves all of this..
SIAM’SIAM’ss Definition Definition ofof CSE CSEhttp://www.siam.org/cse/report.htmhttp://www.siam.org/cse/report.htm
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CSE makes use of the techniques of applied mathematics and computer CSE makes use of the techniques of applied mathematics and computer science for the science for the development of problem-solving methodologiesdevelopment of problem-solving methodologies and and robust tools which will be the building blocks for solutions to scientific robust tools which will be the building blocks for solutions to scientific and engineering problems of ever-increasing complexity. It and engineering problems of ever-increasing complexity. It differs from differs from mathematics or computer sciencemathematics or computer science in that analysis and methodologies are in that analysis and methodologies are directed directed specificallyspecifically at the solution of problem classes from at the solution of problem classes from science and science and engineeringengineering, and will generally require a detailed knowledge or , and will generally require a detailed knowledge or substantial substantial collaborationcollaboration from those disciplines. The computing and from those disciplines. The computing and mathematical techniques used may be more domain specific, and the mathematical techniques used may be more domain specific, and the computer science and mathematics skills needed will be broader.computer science and mathematics skills needed will be broader. It is It is more thanmore than a scientist or engineer a scientist or engineer using a canned codeusing a canned code to generate and visualize results (skipping all of the to generate and visualize results (skipping all of the intermediate steps).intermediate steps).
SIAM's Definition of CSESIAM's Definition of CSE (2) (2)What is it NOT!What is it NOT!
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Part IIa
Metal Foams Metal Foams
In collaboration with theIn collaboration with theInstitut für Werkstoffwissenschaften Institut für Werkstoffwissenschaften
Lehrstuhl Werkstoffkunde und Technologie der Metalle Lehrstuhl Werkstoffkunde und Technologie der Metalle WTM (R.F. Singer, WTM (R.F. Singer, C. KörnerC. Körner))
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GlassCeramics
MetalsPolymers
Structural Properties stiffness
energy absorption damping
Functional Properties burner, shock absorber,
heat exchanger, batteries
large, dynamic surface expansion
Examples of FoamsExamples of Foams
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Towards Simulating Metal FoamsTowards Simulating Metal Foams
Bubble growth, Bubble growth, coalescence, collapse, coalescence, collapse, drainage,drainage, rheology, etc. are rheology, etc. are still poorly understoodstill poorly understood
• Simulation as a tool to Simulation as a tool to better understand, control better understand, control and optimize the processand optimize the process
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The Lattice-Boltzmann MethodThe Lattice-Boltzmann Method
Based on cellular automataIntroduced by von Neumann around 1940
Famous: Conway’s Game of Life
Complex system with simple rulesRegular grid
Local rules specifying time evolution
Intrinsically parallel for model & simulation, similar to elliptic PDE solvers
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The Lattice-Boltzmann MethodThe Lattice-Boltzmann Method
Weakly compressible approximation of the Navier-Stokes equations
Easy implementation
Applicable for small Mach numbers (< 0.1)
Easy to adapt, e.g. forComplicated or time-varying geometries
Free surfaces
Additional physical and chemical effects
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The Lattice-Boltzmann MethodThe Lattice-Boltzmann MethodReal valued representation of particles
Discrete velocities and positions
Algorithm consists of two steps:
Stream
Collide
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The Stream StepThe Stream Step
Move particle distribution functions along corresponding velocity vector
Normalized time step, cell size, and particle speed
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The Collide StepThe Collide Step
“Computes collisions” of particles in cell
Weigh equilibrium velocities and velocities from streaming depending on fluid viscosity
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LBM DemonstrationLBM Demonstration(Java applet)
file:///Users/ruede/doc/lehr/vorles/ws03/hppt/lbm/jlb-comp/start.html
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Free surfaces with LBMFree surfaces with LBM
Metal Foams – large gas volume
Only simulate and track fluid motion
Compute boundary conditions at free surface
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Free surface implementationFree surface implementation
Before stream step, compute mass exchange across cell boundaries for interface cells
Calculate bubble volumes and pressure
Surface curvature for surface tension
Change topology if interface cells become full or empty – keep layer of interface cells closed
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Curvature calculation (version I)Curvature calculation (version I)
Alternative approaches:
Integrate normals over surface (weighted triangles)
Level set methods (track surface as implicit function)
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Boundary ConditionsBoundary Conditions
Gas
Liquid
Problem: Missing distribution functions at interface cells after streaming!
Reconstruction such that macroscopic boundary conditions are satisfied.
Körner et al. Lattice Boltzmann Model for Free Surface Flow, to be published in Journal of Computational Physics
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Surface Tension (Vers. 2)Surface Tension (Vers. 2)
Vδ
ΑΑΑ −=δ
Α
Α
1ν_3n
_
2n_
Marching-cube surface triangulationCompute a curvature for each triangle
Associate with each LBM cell the average curvature of its triangles
Complicated Beats level sets for our applications (mass conservation).
κ = 12
dA
dV
•
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Free surface flow: Breaking DamFree surface flow: Breaking Dam
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Rising BubblesRising Bubbles
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More Rising BubblesMore Rising Bubbles
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Simulation VerificationSimulation Verificationby Experimentby Experiment
Simulation and Experiment: Simulation and Experiment: N. ThüreyN. Thürey
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0,000
0,001
0,002
0,003
0,004
0,005
0,006
0,007
0,008
0 50 100
Distance in l.u.
Velocity
Numerical result
Analytical result
Stokes´ Law: Climbing rate of a bubble exposed to gravity
Climb rate
Ideal bubble No boundaries Equilibrium state
R = 8, τ = 0.74, g = 10-4, σ = 2*10-2100 x 100 x 140 cellsExample:
Rel. error: 2 %
Error = function of the system size
Verification for bubble dynamicsVerification for bubble dynamics(C. Körner)(C. Körner)
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True Foams with Disjoining PressureTrue Foams with Disjoining Pressure
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VisualizationVisualization
Ray-tracingRefractionReflectionCausticsAbout 15 Min per frame
= 1 day for 4 secsAbout same compute time as flow simulation
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Part II b
Nanotechnology:Nanotechnology:Interacting Particles in a FluidInteracting Particles in a Fluid
Cooperation withCooperation withW. Peukert, H.J. Schmid W. Peukert, H.J. Schmid
(Chemical Engineering, Particle Technology)(Chemical Engineering, Particle Technology)
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Nano TechnologyNano TechnologyProperties of materials and products determined by structure of the nano-scale particles
Possible applications of the LBM:
Simulate the behavior of particles and particle agglomerates in solutions (e.g. breaking up or further agglomeration)
On a larger scale simulate segregation processes
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Nano TechnologyNano Technology
Curved Boundaries:Particles approximated with spheresImprove accuracy of LBM simulations by using curved boundary conditions
Standard No-SlipReflect DFs at cell boundary
More accurate:Take distance to boundary surface into account, then interpolate DFs accordingly
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Nanotechnology ApplicationsNanotechnology Applications
Fluid-Body Interaction:
Compute the forces acting upon a body due to the fluid flow around it
Integrate DFs towards the body for all cells on its surface
Body-Fluid Interaction:Bodies moving in the fluid
Modify outgoing DFs at the boundary with the surface velocity of the body
C. Feichtinger: Studienarbeit
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Nanotechnology ApplicationsNanotechnology ApplicationsMoving particle agglomerate in the flow
K. Iglberger - just completed Master Thesis Projectand Chr. Feichtinger - Studienarbeit
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Part II c
Biomedical EngineeringBiomedical Engineering
The Inverse EEG ProblemThe Inverse EEG Problem
with M. Mohr and C. Freundlwith M. Mohr and C. Freundl
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Bio-electric Field ComputationsBio-electric Field Computations
Reconstruction of electromagnetic fieldsReconstruction of electromagnetic fields from EEG-Measurements:from EEG-Measurements:
Source LocalizationSource Localization
NeurosurgeryNeurosurgeryKopfklinikum ErlangenKopfklinikum Erlangen
View throughView throughoperation microscopeoperation microscope
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Why simulate and not experiment?Why simulate and not experiment?
Open brain EEG-Open brain EEG-Measurements for Measurements for
LocalizingLocalizing functional brain regions functional brain regions
Simulation basedSimulation basedVirtual operation planningVirtual operation planning
Image: Chr. Johnson, Salt Lake City
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Problem of inverse EEG/MEGProblem of inverse EEG/MEGDirect Problem: Direct Problem:
• Known:Known: Sources (strength, Sources (strength, position, orientation)position, orientation)
• Wanted:Wanted: Potentials on the Potentials on the head surfacehead surface
• Inverse ProblemInverse Problem• Known:Known: Potentials on the Potentials on the
head surfacehead surface• Wanted:Wanted: Sources (strength, Sources (strength,
position, orientation)position, orientation)
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Source LocalizationSource Localization3D MRI data3D MRI data
512 x 512 x 256512 x 512 x 256voxelsvoxels
segmentationsegmentation4 compartmens4 compartmens
Localized Localized Epileptic focusEpileptic focus
Dipole localizationDipole localizationsearch algorithmsearch algorithm = optimization= optimization
Collaborators: Univ. of Utah (Chris Johnson), Ovidius Univ. Constanta (C. Popa)Collaborators: Univ. of Utah (Chris Johnson), Ovidius Univ. Constanta (C. Popa)Bart Vanrumste (Gent, Univ. of Canterbury, New Zealand), G. Greiner, F. FahlbuschBart Vanrumste (Gent, Univ. of Canterbury, New Zealand), G. Greiner, F. Fahlbusch
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Part IIIa
High Performance ComputingHigh Performance ComputingTrends in High End ComputingTrends in High End Computing
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Simulation isSimulation is
Performance hungry andMemory intensiveParallel Supercomputing required
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Supercomputer Performance: TOP 500 ListSupercomputer Performance: TOP 500 List
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Earth Simulator (Japan)36 TFlop
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Columbia Supercomputer(NASA)52 TFlops
IBM Blue Gene/L and its CompetitorsIBM Blue Gene/L and its Competitors
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Architecture example: Our Pet DinosaurArchitecture example: Our Pet Dinosaur
8 Proc and 8 GB per node8 Proc and 8 GB per node
Performance:Performance: 1344 CPUs (168*8) 1344 CPUs (168*8) 12 GFlop/node12 GFlop/node 2016 GFlop total2016 GFlop total Linpack: 1645 Gflop Linpack: 1645 Gflop
(82% of theoretical peak) (82% of theoretical peak) Very sensitive to data Very sensitive to data
structuresstructures To be replaced by a 6000 Proc. To be replaced by a 6000 Proc.
SGI in 1Q 2006;SGI in 1Q 2006; upgrade to >70 Tflop in 2007upgrade to >70 Tflop in 2007
Hitachi SR 8000Hitachi SR 8000 at the Leibniz-Rechenzentrum derat the Leibniz-Rechenzentrum der
Bayerischen Akademie der Bayerischen Akademie der WissenschaftenWissenschaften
(#5 at time of installation in 2000, now #273)(#5 at time of installation in 2000, now #273)
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LSS Cluster-ComputerLSS Cluster-Computer
Fujitsu-Siemens HPC LineFujitsu-Siemens HPC Line
Programming MethodsProgramming MethodsCache Optimization Cache Optimization
C++ Expression TemplatesC++ Expression Templates
(Parallel) Algorithms(Parallel) Algorithms
Cooperations inCooperations inMaterial SciencesMaterial Sciences
EngineeringEngineering• MechanicalMechanical• ElectricalElectrical• ChemicalChemical
Medical TechnologyMedical Technology
. . .. . .
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LSSLSS-Cluster-ClusterCompute Nodes (8x4 CPUs)Compute Nodes (8x4 CPUs)
CPU: AMD Opteron 848 2.2 GHz, max. 4.4 GFlops
RAM:16 GByte
Interactive Nodes (9x2 CPUs)Interactive Nodes (9x2 CPUs) CPU:
AMD Opteron 248
High-Speed Network InfiniBandHigh-Speed Network InfiniBand
10 GBit/s
Fujitsu-SiemensFujitsu-Siemens
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V10.000.000.000
1.000.000.000
100.000.000
10.000.000
1.000.000
100.000
1.000
10.000
100
4004
80368
Pentium
Merced
1K
64K
256K
1M4M
64M
1G
4G
1970 1975 1980 1985 1990 1995 2000 2005
Year
Tra
ns
isto
rs/D
ie
Microprocessor(Intel)
DRAM
Growth:42% per year
Growth:52% per year
Moore's Law in Semiconductor Technology(F. Hossfeld)
80468
Pentium Pro
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1021
1018
1015
1012
109
1024
103
106
1
1950 1960 1970 1980 1990 2000 2010 2020
Year
Ato
ms/
Bit
Information Density & Energy Dissipation(adapted by F. Hossfeld from C. P. Williams et al., 1998)
10 -9
10 -6
10 -3
1
10 3
10 6
10 9
1012
1015
En
erg
y/lo
gic
Op
era
tion
[p
ico
-Jou
les]
kT
Semiconductor Technology
≈ 2017
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Current Challenge:Current Challenge:Parallelism on all levels andParallelism on all levels and
The Memory WallThe Memory Wall
Parallel computing is easy, good (single) processor performance is Parallel computing is easy, good (single) processor performance is difficult (B. Gropp, Argonne)difficult (B. Gropp, Argonne)
There has been no significant progress in High Performance Computing There has been no significant progress in High Performance Computing
over the past 5 years (H. Simon, NERSC)over the past 5 years (H. Simon, NERSC)
Instruction level parallelismInstruction level parallelism
Memory bandwidth and latencyMemory bandwidth and latency are the limiting factors are the limiting factors
Cache-aware algorithmsCache-aware algorithms
Conventional Conventional complexity measurescomplexity measures (based on operation count) are (based on operation count) are
becoming increasingly becoming increasingly unrealisticunrealistic..
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Part IIIb
High Performance ComputingHigh Performance ComputingHierarchical Hybrid Grids (HHG)Hierarchical Hybrid Grids (HHG)
with B. Bergen and F. Hülsemannwith B. Bergen and F. Hülsemann
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Structured vs. Unstructured Grids(on Hitachi SR 8000)
gridlib/HHG MFlops rates for matrix-vector multiplication on one node on the Hitachi
compared with highly tuned JDS results for sparse matrices (courtesy of G. Wellein, RRZE Erlangen)
0
1000
2000
3000
4000
5000
6000
7000
8000
729 35,937 2,146,689 # unknowns
JDSStencils
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What are hierarchical hybrid grids?What are hierarchical hybrid grids?
Standard geometric multigrid approach:Standard geometric multigrid approach:Purely unstructured input gridPurely unstructured input grid
resolves geometry of problem domainresolves geometry of problem domainPatch-wise regular refinementPatch-wise regular refinement
applied repeatedly to every cell of the coarse gridapplied repeatedly to every cell of the coarse gridgenerates nested grid hierarchies naturally suitable generates nested grid hierarchies naturally suitable for geometric multigrid algorithmsfor geometric multigrid algorithms
New: New: Modify storage formats and operations on the grid to Modify storage formats and operations on the grid to exploit the exploit the regular substructuresregular substructures
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Common misconceptionsCommon misconceptions
Hierarchical hybrid grids (HHG) Hierarchical hybrid grids (HHG) are not yet another block structured gridare not yet another block structured grid
HHG are more flexible (HHG are more flexible (unstructured, hybrid unstructured, hybrid input gridsinput grids))
are not yet another unstructured geometric multigrid are not yet another unstructured geometric multigrid packagepackage
HHG achieve better performance -- HHG achieve better performance -- unstructured treatment of regular regions does unstructured treatment of regular regions does not improve performancenot improve performance
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Refinement example
Input Grid
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Refinement example
Refinement Level one
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Refinement example
Refinement Level Two
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Refinement example
Structured InteriorStructured Interior
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Refinement example
Structured Interior
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Refinement example
Edge Interior
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Refinement example
Edge Interior
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Problems and Solutions
Problems with C++ on HitachiOnly alpha version quality of C++
Excessive compile times
Poor code quality
Solution for gridlib-HHGconservative C++
resorting to mixed language programming C++/F77 (after painful experience)
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Results, Scaling, EfficiencyResults, Scaling, Efficiency(results by F. Hülsemann, Ben Bergen)(results by F. Hülsemann, Ben Bergen)
Brick-shaped Finite elementsBrick-shaped Finite elements
Poisson equationDirichlet boundary conditionsMultigrid FMG(2,2) cycle27 point stencil9 cubes/processrefinement level 7 (h=1/128)
Speedup for the same problem
(6 times regularly refined)
4810139.49550
459438.94512
444719.47256
442359.74128
441179.4864
Time (s)Dof x 106#CPU
0
5
10
15
20
25
30
35
0 20 40 60 80Number of processes
Linear Observed
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Performance on SGI Altix forPerformance on SGI Altix for Tetrahedral HHG-Mesh Tetrahedral HHG-Mesh
Scale-up test: Compute time vs. Proc #Problem size
2 Proc: 66 Mio unknowns512 & 1024 Proc: 17,000 Mio. unknowns
Bergen, Hülsemann, UR: Is 1.7×1010 unknowns the largest Finite Element system that can be solved today? accepted to Supercomputing in Nov ´05.
Per Proc. Performance
Smoothing aloneComplete V(3,3) MG cycle
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Part IIIc
High Performance ComputingHigh Performance ComputingParallel Free Surface LBM-MethodsParallel Free Surface LBM-Methods
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Parallelization of LBM CodeParallelization of LBM CodeStandard LBM-Code in C (1-D Partitioning):
- excellent performance on single SR8000 node- almost linear speed-up- large partitions favorable
Performance on SR8000
Ca. 30% of Peak Performance
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ParallelisationParallelisation
Standard LBM-Code: Scalability
Largest Simulation:1,08*109 cells
370 GByte memory
Communication Cost because of large data volume (64 MByte)
Efficiency ~ 75%
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ParallelisationParallelisation
Free surface LBM-Code
Standard LBM Free surface LBM
1 sweep through grid 5 sweeps through grid
Cell type changes, Closed boundary for bubbles, Initialization of modified cells, Mass balance correction
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ParallelisationParallelisation
Free surface LBM-Code:
Standard LBM Free surface LBM
1 sweep through grid 5 sweeps through grid
1 row of ghost nodes 4 rows of ghost nodes
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PerformancePerformanceFree surface LBM-Code Free surface LBM-Code
Standard LBM-CodeStandard LBM-Code
Performance lousy on a single node! Conditionals: 2,9 SLBM 51 free surface LBMPentium 4: almost no degradation ~ 10%SR 8000: enormous degradation (pseudo-vector, predictable jumps)
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Part IV
ConclusionsConclusions
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Conclusions (1)Conclusions (1)High performance simulation still requires
“heroic programming”Parallel Programming is easy, node performance is difficult (B. Gropp, Argonne)Which architecture ?
ASCI-type: custom CPU, massively parallel cluster of SMPs• nobody has been able to show that these machines scale efficiently,
except on a few very special applications and using enormous human effort
Earth-simulator-type: Vector CPU, as many CPUs as affordable• impressive performance on vectorizable code, but need to check with
more demanding data and algorithm structuresHitachi Class: modified custom CPU, cluster of SMPs
• excellent performance on some codes, but unexpected slowdowns on others, too exotic to have a sufficiently large software base
Others: BlueGene, Cray X1, Multithreading, PIM, reconfigurable …, quantum computing, …
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Conclusions (2)Conclusions (2)Which data structures?
structured (inflexible) unstructured (slow)HHG (high development effort, even prototype 50 K lines of code)meshless … (useful in niches)
Where are we going?the end of Moore’s lawnobody builds CPUs with numerical simulation requirements high on the list of priorities.petaflops: 100,000 processors and we can hardly handle 1000It’s the locality - stupid!the memory wall
• latency• bandwidth
Distinguish between algorithms where control flow is• data independent: latency hiding techniques(pipelining, prefetching, etc)
can help• data dependent
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In the Future?In the Future?
What’s beyond Moore’s Law?What’s beyond Moore’s Law?
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Part VI
Outlook: Other applicationsOutlook: Other applications
Computational Steering andComputational Steering andReal-Time simulationReal-Time simulation
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Near-Real-Time Free-Surface LBMNear-Real-Time Free-Surface LBM
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AcknowledgementsAcknowledgementsCollaborators
In Erlangen: WTM, LSE, LSTM, LGDV, LFG, RRZE, etc.Especially for foams: C. Körner (WTM)International: Utah, Technion, Constanta, Ghent, Boulder, ...
Dissertationen ProjectsB. Bergen (HHG)
C. Freundl (Parallel Expression Templates for PDE-solver)
J. Härtlein (Expression Templates for FE-Applications)
N. Thürey (LBM, free surfaces)
... and 6 more
16 Diplom- /Master- ThesisStudien- /Bachelor- Thesis
Especially for Performance-Analysis/ Optimization of the LBM• J. Wilke, K. Iglberger, S. Donath
... and 24 more
KONWIHR, DFG, NATO, BMBFKONWIHR, DFG, NATO, BMBFElitenetzwerk BayernElitenetzwerk Bayern
Bavarian Graduate School in Computational Engineering (with TUM, Jan. 2005)Bavarian Graduate School in Computational Engineering (with TUM, Jan. 2005)Special International PhD program: Identifikation, Optimization and Optimal Control Special International PhD program: Identifikation, Optimization and Optimal Control for Engineering Applications (with Bayreuth and Würzburg) starting for Engineering Applications (with Bayreuth and Würzburg) starting Jan. 06Jan. 06
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Talk is OverTalk is Over
Please wake up!Please wake up!
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ASIMASIMAnnual ConferenceAnnual Conference
18. Symposium18. Symposium
Simulation Simulation TechniquesTechniques
12. - 15. September 200512. - 15. September 2005
in in ErlangenErlangen
www10.informatik.uni-erlangen.de/asim2005/
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Near-Real-Time Free-Surface LBMNear-Real-Time Free-Surface LBM