Advertisement

A Fast Poisson Solver for Hybrid Reconfigurable System

  • Vitor Gomes
  • Haroldo Campos Velho
  • Andrea Charão
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7806)

Abstract

This paper presents the design and implementation of a fast Poisson solver on a reconfigurable hybrid system. Our hybrid solver integrates a FPGA-based FFT coprocessor to collaborate in the solution of a numerical meteorological model involving one-dimensional shallow water equations. The Poisson equation is solved using a singular value decomposition associated with the Moore-Penrose inverse. The hybrid fast Poisson solver is evaluated under different amount of data entry and shows performance gains compared to the reference application.

Keywords

Fast Poisson Solver Hybrid Reconfigurable Systems FPGA 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Campbell, S., Meyer, C.: Generalized Inverses of Linear Transformations, ser. Classics in Applied Mathematics. Society for Industrial and Applied Mathematics (2009)Google Scholar
  2. 2.
    de Velho, H.F.C., Claeyssen, J.C.R.: Singular value decomposition in the numerical integration of an atmospheric model. In: XIII Iberian Latin American Congress on Computational Methods in Engineering, CILAMCE 1992, Porto Alegre, RS, BR, pp. 344–353 (1992)Google Scholar
  3. 3.
    Davids, P.J.: Circulant Matrices. John Wiley & Sons, New York (1979)Google Scholar
  4. 4.
    Cooley, J.W., Tukey, J.W.: An Algorithm for the Machine Calculation of Complex Fourier Series. Mathematics of Computation 19(90), 297–301 (1965), http://dx.doi.org/10.2307/2003354 zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Takahashi, D., Kanada, Y.: High-Performance Radix-2, 3 and 5 Parallel 1-D Complex FFT Algorithms for Distributed-Memory Parallel Computers. J. Supercomput. 15(2), 207–228 (2000)zbMATHCrossRefGoogle Scholar
  6. 6.
    Hemmert, K.S., Underwood, K.D.: An Analysis of the Double-Precision Floating-Point FFT on FPGAs. In: Annual IEEE Symposium on Field-Programmable Custom Computing Machines, pp. 171–180 (2005)Google Scholar
  7. 7.
    Cray Inc., Design of Cray XD1 QDR II SRAM Core, Mendota, MN, USA (2005)Google Scholar
  8. 8.
    Brodtkorb, A.R., Dyken, C., Hagen, T.R., Hjelmervik, J.M., Storaasli, O.O.: State-of-the-art in heterogeneous computing. Sci. Program. 18, 1–33 (2010)Google Scholar
  9. 9.
    Hu, J.: Solution of partial differential equations using reconfigurable computing. Ph.D. dissertation, University of Birmingham (December 2011), http://etheses.bham.ac.uk/1655/
  10. 10.
    Zhuo, L., Prasanna, V.K.: High Performance Linear Algebra Operations on Reconfigurable Systems. In: SC 2005: Proc. of the 2005 ACM/IEEE Conference on Supercomputing. IEEE Computer Society, Washington, DC (2005)Google Scholar
  11. 11.
    Bondhugula, U., Devulapalli, A., Dinan, J., Fernando, J., Wyckoff, P., Stahlberg, E., Sadayappan, P.: Hardware/Software Integration for FPGA-based All-Pairs Shortest-Paths. In: FCCM 2006: Proc. of the 14th Annual IEEE Symposium on Field-Programmable Custom Computing Machines, pp. 152–164. IEEE Computer Society, Washington, DC (2006)CrossRefGoogle Scholar
  12. 12.
    Lynch, P.: DYNAMO—A one dimensional primitive equation model. Dublin, Irlanda, Tech. Rep. (1984)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Vitor Gomes
    • 1
  • Haroldo Campos Velho
    • 1
  • Andrea Charão
    • 2
  1. 1.Laboratory of Computing and Applied MathematicsBrazilian Institute for Space ResearchSão José dos CamposBrazil
  2. 2.Computer Systems LaboratoryFederal University of Santa MariaSanta MariaBrazil

Personalised recommendations