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The parallel solution of nonsymmetric sparse linear systems using the H* reordering and an associated factorization

In this paper, a nonsymmetric sparse linear system solver based on the exploitation of multilevel parallelism is proposed. One of the main issues addressed is the application of tearing techniques to enhance large grain parallelism in a manner that maintains reasonable stability. This is accomplished by a combination of a novel reordering technique (H*) and pivoting strategy. The large grain parallelism exposed by the reordering is combined with medium (various parallel row updates strategies) and fine grain (vectorization) parallelism to allow adaptation to a wide range of multiprocessor architectures. Experimental results are presented which show the effectiveness of the reordering, as well as the stability and efficiency of the solver.