A binary tree implementation of a parallel distributed tridiagonal solver
Parallel Computing
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ACM SIGARCH Computer Architecture News
Relationships Between Efficiency and Execution Time of Full Multigrid Methods on Parallel Computers
IEEE Transactions on Parallel and Distributed Systems
Message Passing Evaluation and Analysis on Cray T3E and SGI Origin 2000 Systems
Euro-Par '99 Proceedings of the 5th International Euro-Par Conference on Parallel Processing
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ICPP '99 Proceedings of the 1999 International Conference on Parallel Processing
Robust multigrid smoothers for three dimensional elliptic equations with strong anisotropies
Robust multigrid smoothers for three dimensional elliptic equations with strong anisotropies
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In this paper two well-known robust multigrid solvers for anisotropic operators on structured grids are compared: alternating-plane smoothers with full coarsening and plane smoothers combined with semicoarsening. The study takes into account not only numerical properties but also architectural ones, focusing on cache memory exploitation and parallel characteristics. Experimental results for the sequencial algorithms have been obtained on two different systems based on the MIPS R10000 processor but with different L2 cache sizes (an SGI O2 workstation and an SGI Origin 2000 system). Two different parallel implementations for the latter robust approach have been considered. The first one has optimal parallel characteristics but due to deterioration of the convergence properties its realistic efficiency is not satisfactory. In the second one, some processors remain idle during a short period of time on every multigrid cycle, however the algorithm is more efficient since it preserves the numerical properties of the sequencial version. Parallel experiments have also been taken on a Cray T3E system.