A Large-Grain Parallel Sparse System Solver

Abstract

. The efficiency of solving sparse linear systems on parallel processors and more complex multicluster architectures such as Cedar is greatly enhanced if relatively large grain computational tasks can be assigned to each cluster or processor. The ordering of a system into a bordered block upper triangular form facilitates a reasonable large-grain partitioning. A new algorithm which produces this form for unsymmetric sparse linear systems is considered and the associated factorization algorithm is presented. Computational results are presented for the Cedar multiprocessor. Several techniques have been proposed to solve large sparse systems of linear equations on parallel processors. A key task which determines the effectiveness of these techniques is the identification and exploitation of the computational granularity appropriate for the target multiprocessor architecture. Many algorithms assume special properties such as symmetric positive definiteness or exploit knowledge of the appl..