Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2012, Special Issue (2012), Article ID 365124, 9 pages.

A Modified SSOR Preconditioning Strategy for Helmholtz Equations

Shi-Liang Wu and Cui-Xia Li

Full-text: Open access

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.

Article information

Source
J. Appl. Math., Volume 2012, Special Issue (2012), Article ID 365124, 9 pages.

Dates
First available in Project Euclid: 3 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.jam/1357179947

Digital Object Identifier
doi:10.1155/2012/365124

Mathematical Reviews number (MathSciNet)
MR2861936

Zentralblatt MATH identifier
1235.65126

Citation

Wu, Shi-Liang; Li, Cui-Xia. A Modified SSOR Preconditioning Strategy for Helmholtz Equations. J. Appl. Math. 2012, Special Issue (2012), Article ID 365124, 9 pages. doi:10.1155/2012/365124. https://projecteuclid.org/euclid.jam/1357179947


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