Efficient Parallel Solutions of Large Sparse SPD Systems on Distributed-memory Multiprocessors
Chunguang Sun · eCommons (Cornell University) · 1992
. We consider several issues involved in the solution of sparse symmetric positive definite systems 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 a 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 three-dimensional grid problem on an iPSC/860 machine with 32 processors. Key words. Cholesky factorization, clique tree, distributed-memory multiprocessors, multifro...