Maximizing cache memory usage for multigrid algorithms for applications of fluid flow in porous media

  • Douglas C
  • Hu J
  • Iskandarani M
 et al. 
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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.

Author-supplied keywords

  • multigrid; cache; threads; sparse matrix; iterativ

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Authors

  • Craig C Douglas

  • Jonathan Hu

  • Mohamed Iskandarani

  • Markus Kowarschik

  • Ulrich Rüde

  • Christian Weiss

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