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

作者：Zhang Zhengyi^*; Sameh Ahmed H

来源：Computers & Mathematics with Applications, 2016, 72(8): 2000-2007.

DOI：10.1016/j.camwa.2016.08.016

• Numerical linear algebra
• Krylov subspace methods
• Preconditioners
• Hermitian/Skew-Hermitian splitting
• Parallel numerical algorithms

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.

• 出版日期2016-10