A Modified SSOR Preconditioning Strategy for Helmholtz Equations
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 strat...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/365124 |
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| _version_ | 1849695914686414848 |
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| author | Shi-Liang Wu Cui-Xia Li |
| author_facet | Shi-Liang Wu Cui-Xia Li |
| author_sort | Shi-Liang Wu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-d09f95424e1f42f180901065196db69a |
| institution | DOAJ |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-d09f95424e1f42f180901065196db69a2025-08-20T03:19:36ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/365124365124A Modified SSOR Preconditioning Strategy for Helmholtz EquationsShi-Liang Wu0Cui-Xia Li1College of Mathematics, Chengdu University of Information Technology, Chengdu 610225, ChinaSchool of Mathematics and Statistics, Anyang Normal University, Anyang 455002, ChinaThe 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.http://dx.doi.org/10.1155/2012/365124 |
| spellingShingle | Shi-Liang Wu Cui-Xia Li A Modified SSOR Preconditioning Strategy for Helmholtz Equations Journal of Applied Mathematics |
| title | A Modified SSOR Preconditioning Strategy for Helmholtz Equations |
| title_full | A Modified SSOR Preconditioning Strategy for Helmholtz Equations |
| title_fullStr | A Modified SSOR Preconditioning Strategy for Helmholtz Equations |
| title_full_unstemmed | A Modified SSOR Preconditioning Strategy for Helmholtz Equations |
| title_short | A Modified SSOR Preconditioning Strategy for Helmholtz Equations |
| title_sort | modified ssor preconditioning strategy for helmholtz equations |
| url | http://dx.doi.org/10.1155/2012/365124 |
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