Preconditioned Krylov Solvers and Methods for Runtime Loop Parallelization

摘要

We make a detailed examination of the performance achieved by a Krylov space sparse linear system solver that uses incompletely factored matrices for preconditioners. We compared two related mechanisms for parallelizing the computationally critical sparse triangular solves and sparse numeric incomplete factorizations on a range of test problems. From these comparisons we drew several interesting conclusions about methods that can be used to parallelize loops of the type found here. The performance we obtain is brought into perspective by comparison with timing results from a Cray X/MP supercomputer. Performance on an Encore Multimax/320 with relatively modest computational capabilities comes within a small factor of the performance on a comparable code run on a Cray X/MP. (KR)