Abstract
This paper summarizes theoretical and practical investigations into the effect of parallelization by grid-partitioning on the performance of multigrid methods for the solution of partial differential equations on general two-dimensional domains. Particular emphasis will be placed on the algorithmic scalability for MIMD distributed memory systems. Experimental results for two Navier-Stokes test problems, presented in the last section of the paper, show that the theoretically predicted dependency of the combined numerical and parallel efficiencies of multigrid methods on the number of processors employed is in fact very weak. This leads to the conclusion that multigrid is an appropriate candidate for solving partial differential equations on massively parallel machines.
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