TY - JOUR T1 - An Iterative Two-Grid Method of a Finite Element PML Approximation for the Two Dimensional Maxwell Problem AU - Liu , Chunmei AU - Shu , Shi AU - Huang , Yunqing AU - Zhong , Liuqiang AU - Wang , Junxian JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 175 EP - 189 PY - 2012 DA - 2012/04 SN - 4 DO - http://doi.org/10.4208/aamm.10-m11166 UR - https://global-sci.org/intro/article_detail/aamm/113.html KW - Maxwell scattering, edge finite element, PML, iterative two-grid method. AB -

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.