Efficient implementation of the multigrid preconditioned conjugate gradient method on distributed memory machines

Authors:
Osamu Tatebe;Yoshio Oyanagi
Affiliations:
University of Tokyo, Bunkyo-ku, Tokyo 113, JAPAN;University of Tokyo, Bunkyo-ku, Tokyo 113, JAPAN
Venue:
Proceedings of the 1994 ACM/IEEE conference on Supercomputing
Year:
1994

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Abstract

A multigrid preconditioned conjugate gradient (MGCG) method[15], which uses the multigrid method as a preconditioner for the CG method, has a good convergence rate even for the problems on which the standard multigrid method does not converge efficiently. This paper considers a parallelization of the MGCG method and proposes an efficient parallel MGCG method on distributed memory machines. For the good convergence rate of the MGCG method, several difficulties in parallelizing the multigrid method are successfully settled. Besides, the parallel MGCG method on Fujitsu multicomputer AP1000[8] has high performance and it is more than 10 times faster than the Scaled CG (SCG) method[6].