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

作　　者：Chunmei Liu Shi Shu Yunqing Huang Liuqiang Zhong Junxian Wang 

机构地区：[1]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 [2]School of Mathematical Sciences,South China Normal University,Guangzhou 510631,China

出　　处：《Advances in Applied Mathematics and Mechanics》2012年第2期175-189,共15页应用数学与力学进展（英文）

基　　金：This work was partially supported by NSFC Project(Grant No.11031006,91130002,11171281,10971059,11026091);the Key Project of Scientific Research Fund of Hunan Provincial Science and Technology Department(Grant No.2011FJ2011);Hunan Provincial Innovation Foundation for Postgraduate(CX2010B245,CX2010B246).

摘　　要：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.

关 键 词：Maxwell scattering edge finite element PML iterative two-grid method 

分 类 号：O24[理学—计算数学]