Towards Cache-Optimized Multigrid Using Patch-Adaptive Relaxation

Most of today's computer architectures employ fast, yet relatively small cache memories in order to mitigate the effects of the constantly widening gap between CPU speed and main memory performance. Efficient execution of numerically intensive programs can only be expected if these hierarchical memory designs are respected. Our work targets the optimization of the cache performance of multigrid codes. The research efforts we will present in this paper first cover transformations that may be automized and then focus on fundamental algorithmic modifications which require careful mathematical analysis. We will present experimental results for the latter.

[1]  Ulrich Rüde,et al.  Cache Optimization for Structured and Unstructured Grid Multigrid , 2000 .

[2]  Markus Kowarschik,et al.  Data locality optimizations for iterative numerical algorithms and cellular automata on hierarchical memory architectures , 2004, Advances in simulation.

[3]  David Loshin.  Efficient Memory Programming , 1998 .

[4]  Markus Kowarschik,et al.  An Overview of Cache Optimization Techniques and Cache-Aware Numerical Algorithms , 2002, Algorithms for Memory Hierarchies.

[5]  W. Hackbusch.  Iterative Solution of Large Sparse Systems of Equations , 1993 .

[6]  Markus Schordan,et al.  Parallel object‐oriented framework optimization , 2004, Concurr. Comput. Pract. Exp..

[7]  W. Hackbusch.  Elliptic Differential Equations , 1992 .

[8]  Adolfy Hoisie,et al.  Performance Optimization of Numerically Intensive Codes , 1987 .

[9]  H. Lötzbeyer,et al.  Patch-adaptive multilevel iteration , 1997 .

[10]  David A. Patterson,et al.  Computer Architecture: A Quantitative Approach , 1969 .

[11]  Ken Kennedy,et al.  Optimizing Compilers for Modern Architectures: A Dependence-based Approach , 2001 .

[12]  Chau-Wen Tseng,et al.  Tiling Optimizations for 3D Scientific Computations , 2000, ACM/IEEE SC 2000 Conference (SC'00).

[13]  Ullrich Rüde.  Mathematical and Computational Techniques for Multilevel Adaptive Methods , 1987 .

[14]  Markus Schordan,et al.  Parallel object-oriented framework optimization: Research Articles , 2004 .

[15]  Allen,et al.  Optimizing Compilers for Modern Architectures , 2004 .

[16]  Christian Weiß,et al.  Data locality optimizations for multigrid methods on structured grids , 2001 .