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

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