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ANALYSIS OF BLOCK-SOR ITERATION FOR THE THREE-DIMENSIONAL LAPLACIAN

Part of: Numerical linear algebra

Published online by Cambridge University Press:  04 December 2009

WENJUN ZHENG  and
ZHIQIN ZHAO
WENJUN ZHENG
Affiliation:
School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan, PR China (email: [email protected])
ZHIQIN ZHAO*
Affiliation:
School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan, PR China (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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The successive over-relaxation (SOR) iteration method for solving linear systems of equations depends upon a relaxation parameter. A well-known theory for determining this parameter was given by Young for consistently ordered matrices. In this paper, for the three-dimensional Laplacian, we introduce several compact difference schemes and analyse the block-SOR method for the resulting linear systems. Their optimum relaxation parameters are given for the first time. Analysis shows that the value of the optimum relaxation parameter of block-SOR iteration is very sensitive for compact stencils when solving the three-dimensional Laplacian. This paper provides a theoretical solution for determining the optimum relaxation parameter in real applications.

Keywords

compact stencilblock-SOR iterationoptimum relaxation parameterthree-dimensional Laplacian

MSC classification

Secondary: 65F10: Iterative methods for linear systems
Type
Research Article
Information
The ANZIAM Journal , Volume 50 , Issue 4 , April 2009 , pp. 501 - 512
Copyright
Copyright © Australian Mathematical Society 2009

References

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