Improved PHSS iterative methods for solving saddle point problems

被引：0
作者：
Ke Wang
Jingjing Di
Don Liu
机构：
[1] Shanghai University,Department of Mathematics, College of Sciences
[2] Louisiana Tech University,Mathematics & Statistics and Mechanical Engineering
来源：
Numerical Algorithms | 2016年 / 71卷
关键词：
Saddle point problem; Gauss-Seidel method; Uzawa method; PHSS method; Preconditioning;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
An improvement on a generalized preconditioned Hermitian and skew-Hermitian splitting method (GPHSS), originally presented by Pan and Wang (J. Numer. Methods Comput. Appl. 32, 174–182, 2011), for saddle point problems, is proposed in this paper and referred to as IGPHSS for simplicity. After adding a matrix to the coefficient matrix on two sides of first equation of the GPHSS iterative scheme, both the number of required iterations for convergence and the computational time are significantly decreased. The convergence analysis is provided here. As saddle point problems are indefinite systems, the Conjugate Gradient method is unsuitable for them. The IGPHSS is compared with Gauss-Seidel, which requires partial pivoting due to some zero diagonal entries, Uzawa and GPHSS methods. The numerical experiments show that the IGPHSS method is better than the original GPHSS and the other two relevant methods.
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页码：753 / 773
页数：20
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