A parallel sparse linear system solver based on Hermitian/skew-Hermitian splitting

Abstract

In this paper we describe a parallel algorithm for solving large sparse nonsingular linear systems Ax=f, of order n, using the Hermitian Skew-Hermitian splitting approach for handling the augmented linear system, of order 2n, that arises from the linear least problem of minimizing the 2-norm of (f−Ax). We use the restarted GMRES as the outer iteration with the Hermitian Skew-Hermitian Splitting (HSS) preconditioner. In solving systems involving this preconditioner, the most time consuming part deals with handling shifted skew-symmetric systems. We solve such systems using the successive overrelaxation (SOR). Theoretical analysis shows that our solver always converges to the unique solution of Ax=f. We present several numerical experiments that demonstrate the robustness of our solver compared to other schemes, and show its parallel scalability on a single multicore node.