Parallel pivots LU algorithm on the cray T3E

Abstract

Solving large nonsymmetric sparse linear systems on distributed memory multiprocessors is an active research area. We present a loop-level parallelized generic LU algorithm which comprises analysefactorize and solve stages. To further exploit matrix sparsity and parallelism, the analyse step looks for a set of compatible pivots. Sparse techniques are applied until the reduced submatrix reaches a threshold density. At this point, a switch to dense routines takes place in both analyse-factorize and solve stages. The SPMD code follows a sparse cyclic distribution to map the system matrix onto a P× Q processor mesh. Experimental results show a good behavior of our sequential algorithm compared with a standard generic solver: the MA48 routine. Additionally, a parallel version on the Cray T3E exhibits high performance in terms of speed-up and efficiency.