Parallel SAS multicluster algorithms for solving linear systems with reflexive coefficient matrices
Hsin-Chu Chen · 1992
The SAS domain decomposition is an efficient scheme for the numerical solution of a wide class of discretized physical problems on either sequential or vector computers. It is also an amazingly parallelizable approach for multiprocessors like the Cray X–MP, the Cray–2, and the Alliant FX/80, or for multicluster machines of the Cedar type. The efficiency and parallelizability of this scheme for solving symmetric elasticity problems and slightly perturbed asymmetric problems have been demonstrated using an Alliant minisupercomputer which has only two levels of parallelism. For multiprocessors with parallelism of three levels such as the Cedar, this method offers much more freedom for the problem to be solved using all levels of parallelism. In this paper, we provide some strategies for the implementation of this domain decomposition method on multiprocessors of the Cedar type. Three parallel multicluster algorithms for solving linear systems with reflexive coefficient matrices are presented. The main difference among these algorithms lies in the use of the global memory and the cluster memories of the Cedar multicluster processor. The performance of these algorithms on the Cedar using the linear system derived from a 3D elasticity problem with two planes of reflexive symmetry is reported.