Highly Scalable Parallel Algorithms for Sparse Matrix Factorization
IEEE Transactions on Parallel and Distributed Systems
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We consider several issues involved in the solution of sparse symmetric positive definite system by multifrontal method on distributed-memory multiprocessors. First, we present a new algorithm for computing the partial factorization of a frontal matrix on a subset of processors which significantly improves the performance of a distributed multifrontal algorithm previously designed. Second, new parallel algorithms for computing sparse forward elimination and sparse backward substitution are described. The new algorithms solve the sparse triangular systems in multifrontal fashion. Numerical experiments run on an Intel iPSC/860 and an Intel iPSC/2 for a set of problems with regular and irregular sparsity structure are reported. More than 180 million flops per second during the numerical factorization are achieved for a threedimensional grid problem on an iPSC/860 machine with 32 processors.