Volume 4, Issue 2
An Iterative Two-Grid Method of A Finite Element PML Approximation for the Two Dimensional Maxwell Problem

Chunmei Liu ,  Shi Shu ,  Yunqing Huang ,  Liuqiang Zhong and Junxian Wang


Adv. Appl. Math. Mech., 4 (2012), pp. 175-189.

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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.

  • History

Published online: 2012-04

  • AMS Subject Headings

65F10, 65N30, 78A46

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