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

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

Year:    2012

Author:    Chunmei Liu, Shi Shu, Yunqing Huang, Liuqiang Zhong, Junxian Wang

Advances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 2 : pp. 175–189

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 $\boldsymbol{H}(curl)$-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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.10-m11166

Advances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 2 : pp. 175–189

Published online:    2012-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    15

Keywords:    Maxwell scattering edge finite element PML iterative two-grid method.

Author Details

Chunmei Liu

Shi Shu

Yunqing Huang

Liuqiang Zhong

Junxian Wang