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

被引：0
|
作者：
Zheng, Wenjun [1 ]
Zhao, Zhiqin [1 ]
机构：
[1] Univ Elect Sci & Technol China, Sch Elect Engn, Chengdu 610054, Sichuan, Peoples R China
来源：
ANZIAM JOURNAL | 2009年 / 50卷 / 04期
关键词：
compact stencil; block-SOR iteration; optimum relaxation parameter; three-dimensional Laplacian;
D O I：
10.1017/S1446181109000261
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：501 / 512
页数：12
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