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

Author

Tatebe, Osamu ; Oyanagi, Yoshio

Author_Institution

Dept. of Inf. Sci., Tokyo Univ., Japan

fYear

1994

fDate

14-18 Nov 1994

Firstpage

194

Lastpage

203

Abstract

A multigrid preconditioned conjugate gradient (MGCG) method, which uses the multigrid method as a preconditioner for the conjugate gradient method, has a good convergence rate even for 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 a good convergence rate of the MGCG method, several difficulties in parallelizing the multigrid method are successfully settled. It is also shown that the parallel MGCG method has high performance on the Fujitsu AP1000 multicomputer, and it is more than 10 times faster than the scaled conjugate gradient (SCG) method

Keywords

conjugate gradient methods; convergence of numerical methods; differential equations; distributed memory systems; mathematics computing; parallel algorithms; software performance evaluation; Fujitsu AP1000 multicomputer; convergence rate; distributed memory machines; multigrid preconditioned conjugate gradient method; parallelization; performance; scaled conjugate gradient method; Character generation; Convergence; Gradient methods; Information science; Multigrid methods; Parallel processing; Partitioning algorithms; Poisson equations; Robustness; Vectors;

fLanguage

English

Publisher

ieee

Conference_Titel

Supercomputing '94., Proceedings

Conference_Location

Washington, DC

Print_ISBN

0-8186-6605-6

Type

conf

DOI

10.1109/SUPERC.1994.344279

Filename

344279