Analysis on block diagonal and triangular preconditioners for a PML system of an electromagnetic scattering problem

doi:10.1016/j.camwa.2017.07.026

CSpace

	Analysis on block diagonal and triangular preconditioners for a PML system of an electromagnetic scattering problem
	Huang, Na 1,2,3; Ma, Chang-Feng 2; Zou, Jun 4
	2017-12-01
发表期刊	COMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN	0898-1221
卷号	74 期号:11 页码:2856-2873
摘要	We shall propose several block triangular preconditioners for a PML system of an electromagnetic wave scattering problem and analyze the spectral behavior of the preconditioned systems. When the PML system is discretized by edge element methods, it results in a discrete system with its stiffness matrix being complex, symmetric but indefinite, which can be formulated into a real symmetric but indefinite saddle-point system. In order to preserve the symmetry of the coefficient matrix, we present block triangular preconditioners with two-sided preconditioning for the discrete PML system. We will estimate the lower and upper bounds of positive and negative eigenvalues of the preconditioned matrices, respectively. On the other hand, one may also like to apply some iteration methods for nonsymmetric linear systems in applications although the discrete systems are symmetric. To this end, we propose a block triangular preconditioner to precondition the systems only from one side and analyze the spectrum of the preconditioned systems. In addition, we have also established a spectral estimate of the preconditioned system by an effective preconditioner that was recently developed in literature. Numerical experiments are presented to demonstrate the effectiveness and robustness of these new preconditioners and our theoretical predictions on the spectral bounds of the preconditioned systems. (C) 2017 Elsevier Ltd. All rights reserved.
关键词	Maxwell scattering problem PML equations Block triangular preconditioner Spectral distributions
DOI	10.1016/j.camwa.2017.07.026
语种	英语
资助项目	Hi-Tech Research and Development Program of China[2014AA01A302] ; Fujian Normal University ; National Natural Science Foundation of China[11071041] ; National Natural Science Foundation of China[11201074] ; Fujian Natural Science Foundation[2013J01006] ; NSFC/RGC Joint Research Scheme[N_CUHK437/16] ; Hong Kong RGC General Research Fund[405513] ; Hong Kong RGC General Research Fund[14322516]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000418980800015
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/27068
专题	中国科学院数学与系统科学研究院
通讯作者	Zou, Jun
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Fujian Normal Univ, Sch Math & Comp Sci, Fuzhou 350007, Fujian, Peoples R China 3.Fujian Normal Univ, FJKLMAA, Fuzhou 350007, Fujian, Peoples R China 4.Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China
推荐引用方式 GB/T 7714	Huang, Na,Ma, Chang-Feng,Zou, Jun. Analysis on block diagonal and triangular preconditioners for a PML system of an electromagnetic scattering problem[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS,2017,74(11):2856-2873.
APA	Huang, Na,Ma, Chang-Feng,&Zou, Jun.(2017).Analysis on block diagonal and triangular preconditioners for a PML system of an electromagnetic scattering problem.COMPUTERS & MATHEMATICS WITH APPLICATIONS,74(11),2856-2873.
MLA	Huang, Na,et al."Analysis on block diagonal and triangular preconditioners for a PML system of an electromagnetic scattering problem".COMPUTERS & MATHEMATICS WITH APPLICATIONS 74.11(2017):2856-2873.