Solution of Regular, Sparse Triangular Linear Systems on Vector and Distributed-Memory Multiprocessors

摘要

This paper presents the implementations and results of a model problem, the Symmetric Successive Over-Relaxation (SSOR) simulated application benchmark from the NAS Parallel Benchmark suite for three different parallel processors. SSOR is an iterative implicit method that partitions the left hand side matrix into a lower triangular matrix and an upper triangular matrix. The machines used are an eight processor Cray Y-MP, a 32k processor Thinking Machines Corp. CM-2 and a 128 processor Intel iPSC/860. The primary difficulty in implementing SSOR on a parallel machine lies in finding enough parallelism within the triangular solves to keep a large number of processors active. A data mapping useful for distributed memory architectures is presented. The results show that the eight processor Cray Y-MP has the best performance among the three machines.