Analysis of Block-SOR Iteration for the three dimensional Laplacian

Wenjun Zheng, Zhiqin Zhao


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.



Compact Stencil; Block-SOR Iteration; Optimum Relaxation Parameter; Three-dimensional Laplacian


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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.