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

Abstract

Computers today rely heavily on good utilization of their cache memorysubsystems. Compilers are optimized for business applications, notscientific computing ones, however. Automatic tiling of complex numericalalgorithms for solving partial differential equations is simply notprovided by compilers. Thus, absolutely terrible cache performanceis a common result. Multigrid algorithms combine several numericalalgorithms into a more complicated algorithm. In this paper, an algorithmis derived that allows for data to pass through cache exactly onceper multigrid level during a V cycle before the level changes. Thisis optimal cache usage for large problems that do not fit entirelyin cache. The numerical techniques and algorithms discussed in thispaper can be easily applied to numerical simulation of fluid flowsin porous media.