time integration utilities on an fpga cris a. kania with olaf o. storaasli, ph. d. nasa langley

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Time Integration Utilities on an FPGA Cris A. Kania with Olaf O. Storaasli, Ph. D. NASA Langley

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Page 1: Time Integration Utilities on an FPGA Cris A. Kania with Olaf O. Storaasli, Ph. D. NASA Langley

Time Integration Utilities on an FPGA

Cris A. Kaniawith

Olaf O. Storaasli, Ph. D.

NASA Langley

Page 2: Time Integration Utilities on an FPGA Cris A. Kania with Olaf O. Storaasli, Ph. D. NASA Langley

Traditional Computing

• Hardware development has struggled to keep pace with analysis needs

• Computing speed reaching asymptotic limit

• Clusters offer means of faster computing

Moore’s Law

Page 3: Time Integration Utilities on an FPGA Cris A. Kania with Olaf O. Storaasli, Ph. D. NASA Langley

Computing Alternative

• FPGAs offer means to achieve faster execution

• Design is inherently parallel whereas CPUs are sequential

• “Field Programmable” where the circuitry is optimized to best suit the demands of the application

• CPU circuitry 1% active while FPGA circuitry 80% active

Page 4: Time Integration Utilities on an FPGA Cris A. Kania with Olaf O. Storaasli, Ph. D. NASA Langley

Purpose

• Legacy software is incompatible

• Basic engineering utilities must be developed to begin transition

• Critical to many analysis methodologies is the solution to time-dependent PDEs

• Key disciplines which would benefit from an FPGA are CSM and CFD

• Two-fold purpose: Demonstrate the advantages of the FPGA and provide time integration routines

Page 5: Time Integration Utilities on an FPGA Cris A. Kania with Olaf O. Storaasli, Ph. D. NASA Langley

Methods

• Learn Viva programming environment for FPGAs

• Implement time integration schemes for scalar ODEs

• Apply methodology to representative ODE for verification

• Extend utilities for vector PDEs

• Test vector utilities on problems in CFD & CSM

• Compare execution speeds of traditional CPU vs FPGA on identical problems

Page 6: Time Integration Utilities on an FPGA Cris A. Kania with Olaf O. Storaasli, Ph. D. NASA Langley

C/C++ programming environment

VIVA programming environment

Expected 50 to 300 times faster

Page 7: Time Integration Utilities on an FPGA Cris A. Kania with Olaf O. Storaasli, Ph. D. NASA Langley

Accomplishments• Spring-mass system with damping

– four-stage Runge-Kutta integration scheme

– Newmark method

– compare analytical solution with numerical solutions

Page 8: Time Integration Utilities on an FPGA Cris A. Kania with Olaf O. Storaasli, Ph. D. NASA Langley

Accomplishments• Computational Structural Mechanics

– time dependent solution of cantilever beam

• Computational Fluid Dynamics

– time dependent solution quasi-2D flow with area change

Page 9: Time Integration Utilities on an FPGA Cris A. Kania with Olaf O. Storaasli, Ph. D. NASA Langley

Spring-Mass Results• Spring-Mass System with damping

– verified integration schemes on both CPU and FPGA

– numerical solutions agree with analytical solution

– 700 C++ lines, 36 Viva sheets Displacement vs. Time

-10

-5

0

5

10

0 2 4 6 8 10

Time (sec)

Dis

pla

ce

me

nt

Analytical Solution

Numerical Solutions

Page 10: Time Integration Utilities on an FPGA Cris A. Kania with Olaf O. Storaasli, Ph. D. NASA Langley

Cantilever Beam Results

• Cantilever Beam

– solved structural problem using a finite element approach

– used Newmark integration scheme

– 1200 C++ lines, 56+ Viva sheets Elements CPU Solution Time (sec) FPGA Solution Time (sec)

20 109 *40 723 *60 1705 *

Page 11: Time Integration Utilities on an FPGA Cris A. Kania with Olaf O. Storaasli, Ph. D. NASA Langley
Page 12: Time Integration Utilities on an FPGA Cris A. Kania with Olaf O. Storaasli, Ph. D. NASA Langley

Quasi-2D Flow Results

• Quasi-2D Flow– solved fluid dynamics problem involving three simultaneous equations– used Runge-Kutta integration scheme– 700 C++ lines, 49+ Viva sheets

Nodes CPU Solution Time (sec) FPGA Solution Time (sec)60 40 *80 55 *100 66 *140 830 *200 1188 *

Page 13: Time Integration Utilities on an FPGA Cris A. Kania with Olaf O. Storaasli, Ph. D. NASA Langley
Page 14: Time Integration Utilities on an FPGA Cris A. Kania with Olaf O. Storaasli, Ph. D. NASA Langley

Conclusions/Relevancy

• FPGA demonstrates x-fold increase in efficiency over Pentium class CPU

• FPGAs represent next generation hardware

• Numerical integration utilities will aid in transition to FPGA hardware

Page 15: Time Integration Utilities on an FPGA Cris A. Kania with Olaf O. Storaasli, Ph. D. NASA Langley

Acknowledgements

• Dr. Olaf Storaasli, NASA Langley Research Center

• Dr. Arthur Johnson, NASA Langley Research Center

• Mrs. Sue Greiner, New Horizons Governor’s School

Page 16: Time Integration Utilities on an FPGA Cris A. Kania with Olaf O. Storaasli, Ph. D. NASA Langley

Citations

• Meirovitch, L. 1967. Analytical Methods in Vibrations. Macmillan, New York. 555p.

• Anonymous. Unknown Date. The Runge-Kutta Method. <http://www.sst.ph.ic.ac.uk/angus/Lectures/compphys/node11.html>

• Baddourah, M., Storaasli, O., and Bostic, S. Unknown Date. Linear Static Structural and Vibration Analysis on High Performance Computers. International Journal of Computing Systems in Engineering, Vol. 4, No. 4-6, Dec. 1993, pp. 41-49.

• Beckett, P. and Jennings, A. 2002. Towards Nanocomputer Architecture. Proceedings of the 7th Asia-Pacific Computer Systems Architectures Conference, Melbourne, Australia, 2002.

• Cook, R., Malkus, D., and Plesha, M. 1972. Concepts and Applications of Finite Element Analysis 3rd Edition. John Wiley & Sons, Inc. 324p.

• Durbeck, L. and Macias, N. 2001. The Cell Matrix: an architecture for nanocomputing. Nanotechnology, Vol. 12 (2001), pp. 217-230.

• Hoffmann, K. and Chiang, S. 2000. Computational Fluid Dynamics 4th Edition. Engineering Education System. 486p.

• Singleterry, R., Sobieszczanski-Sobieski, J., and Brown, S. 2002. Field-programmable Gate Array Computer in Structural Analysis: An Initial Exploration.

• Storaasli, O., Singleterry, R., and Brown, S. Unknown Date. Scientific Computations on a NASA Reconfigurable Hypercomputer.

• Storaasli, O., Singleterry, R., Sobieski, J., Rutishauser, D. 2002. Importance of Ultrafast Computing for NASA Missions.

• Warsi, S. and Kania, L. 1998. Hybrid Grid Navier-Stokes Solver with H-Refinement Adaptation. AIAA paper 98-0545.

• Watson, W and Storaasli, O. Unknown Date. Application of NASA General-Purpose Solver to Large-Scale Computations in Aeroacoustics. Fifth Symposium on the Large-Scale Analysis and Design and ISE, Williamsburg, VA Oct. 12-15, 1999.

• Anonymous. Unknown Date. Chipping Away. <http://www.forbes.com/forbes/2003/0414/206.html

Page 17: Time Integration Utilities on an FPGA Cris A. Kania with Olaf O. Storaasli, Ph. D. NASA Langley