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Journal of Applied Mathematics
Volume 2012, Article ID 365124, 9 pages
http://dx.doi.org/10.1155/2012/365124
Research Article

A Modified SSOR Preconditioning Strategy for Helmholtz Equations

1College of Mathematics, Chengdu University of Information Technology, Chengdu 610225, China
2School of Mathematics and Statistics, Anyang Normal University, Anyang 455002, China

Received 22 August 2011; Revised 7 November 2011; Accepted 18 November 2011

Academic Editor: Kok Kwang Phoon

Copyright © 2012 Shi-Liang Wu and Cui-Xia Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The finite difference method discretization of Helmholtz equations usually leads to the large spare linear systems. Since the coefficient matrix is frequently indefinite, it is difficult to solve iteratively. In this paper, a modified symmetric successive overrelaxation (MSSOR) preconditioning strategy is constructed based on the coefficient matrix and employed to speed up the convergence rate of iterative methods. The idea is to increase the values of diagonal elements of the coefficient matrix to obtain better preconditioners for the original linear systems. Compared with SSOR preconditioner, MSSOR preconditioner has no additional computational cost to improve the convergence rate of iterative methods. Numerical results demonstrate that this method can reduce both the number of iterations and the computational time significantly with low cost for construction and implementation of preconditioners.