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Time Integration Utilities on an FPGA

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.

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Time Integration Utilities on an FPGA

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

  2. 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

  3. 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

  4. 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

  5. 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

  6. C/C++ programming environment Expected 50 to 300 times faster VIVA programming environment

  7. Accomplishments • Spring-mass system with damping • four-stage Runge-Kutta integration scheme • Newmark method • compare analytical solution with numerical solutions

  8. Accomplishments • Computational Structural Mechanics • time dependent solution of cantilever beam • Computational Fluid Dynamics • time dependent solution quasi-2D flow with area change

  9. 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 Analytical Solution Numerical Solutions

  10. Cantilever Beam Results • Cantilever Beam • solved structural problem using a finite element approach • used Newmark integration scheme • 1200 C++ lines, 56+ Viva sheets

  11. 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

  12. 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

  13. Acknowledgements • Dr. Olaf Storaasli, NASA Langley Research Center • Dr. Arthur Johnson, NASA Langley Research Center • Mrs. Sue Greiner, New Horizons Governor’s School

  14. 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

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