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Maximizing Cache Memory Usage for Multigrid Algorithms for Applications of Fluid Flow in Porous Media

  • Craig C. Douglas
  • Jonathan Hu
  • Mohamed Iskandarani
  • Markus Kowarschik
  • Ulrich Rüde
  • Christian Weiss
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 552)

Abstract

Computers today rely heavily on good utilization of their cache memory subsystems. Compilers are optimized for business applications, not scientific computing ones, however. Automatic tiling of complex numerical algorithms for solving partial differential equations is simply not provided by compilers. Thus, absolutely terrible cache performance is a common result.

Multigrid algorithms combine several numerical algorithms into a more complicated algorithm. In this paper, an algorithm is derived that allows for data to pass through cache exactly once per multigrid level during a V cycle before the level changes. This is optimal cache usage for large problems that do not fit entirely in cache. The numerical techniques and algorithms discussed in this paper can be easily applied to numerical simulation of fluid flows in porous media.

Keywords

multigrid cache threads sparse matrix iterative methods domain decomposition compiler optimization 

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References

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Craig C. Douglas
    • 1
  • Jonathan Hu
    • 2
  • Mohamed Iskandarani
    • 3
  • Markus Kowarschik
    • 4
  • Ulrich Rüde
    • 4
  • Christian Weiss
    • 5
  1. 1.Department of Computer ScienceUniversity of KentuckyLexingtonUSA
  2. 2.Department of MathematicsUniversity of KentuckyLexingtonUSA
  3. 3.Institute of Marine and Coastal SciencesRutgers UniversityNew BrunswickUSA
  4. 4.Lehrstuhl für Systemsimulation (IMMD 10) Institut für InformatikUniversität Erlangen-NürnbergErlangenGermany
  5. 5.Lehrstuhl für Rechnertechnik und Rechnerorganisation (LRR-TUM) Institut für InformatikTechnische Universität MünchenMünchenGermany

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