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An Iterative Two-Grid Method of A Finite Element PML Approximation for the Two Dimensional Maxwell Problem

Published online by Cambridge University Press:  03 June 2015

Chunmei Liu ,
Shi Shu ,
Yunqing Huang ,
Liuqiang Zhong  and
Junxian Wang
Chunmei Liu*
Affiliation:
Hunan Key Laboratory for Computation & Simulation in Science and Engineering and Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education, Xiangtan University, Hunan 411105, China
Shi Shu*
Affiliation:
Hunan Key Laboratory for Computation & Simulation in Science and Engineering and Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education, Xiangtan University, Hunan 411105, China
Yunqing Huang*
Affiliation:
Hunan Key Laboratory for Computation & Simulation in Science and Engineering and Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education, Xiangtan University, Hunan 411105, China
Liuqiang Zhong*
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
Junxian Wang*
Affiliation:
Hunan Key Laboratory for Computation & Simulation in Science and Engineering and Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education, Xiangtan University, Hunan 411105, China
*
URL: http://math.xtu.edu.cn/myphp/math/personal/shushi/, Email: liuchunmei8080@yahoo.com.cn
Corresponding author. Email: shushi@xtu.edu.cn
Email: huangyq@xtu.edu.cn
Email: zhong@scnu.edu.cn
Email: xianxian.student@sina.com
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Abstract

In this paper, we propose an iterative two-grid method for the edge finite element discretizations (a saddle-point system) of Perfectly Matched Layer(PML) equations to the Maxwell scattering problem in two dimensions. Firstly, we use a fine space to solve a discrete saddle-point system of H(grad) variational problems, denoted by auxiliary system 1. Secondly, we use a coarse space to solve the original saddle-point system. Then, we use a fine space again to solve a discrete H(curl)-elliptic variational problems, denoted by auxiliary system 2. Furthermore, we develop a regularization diagonal block preconditioner for auxiliary system 1 and use H-X preconditioner for auxiliary system 2. Hence we essentially transform the original problem in a fine space to a corresponding (but much smaller) problem on a coarse space, due to the fact that the above two preconditioners are efficient and stable. Compared with some existing iterative methods for solving saddle-point systems, such as PMinres, numerical experiments show the competitive performance of our iterative two-grid method.

Keywords

65F1065N3078A46Maxwell scatteringedge finite elementPMLiterative two-grid method
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 4 , Issue 2 , April 2012 , pp. 175 - 189
Copyright
Copyright © Global-Science Press 2012

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