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.