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Analysis on block diagonal and triangular preconditioners for a PML system of an electromagnetic scattering problem
Huang, Na1,2,3; Ma, Chang-Feng2; Zou, Jun4
2017-12-01
Source PublicationCOMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN0898-1221
Volume74Issue:11Pages:2856-2873
AbstractWe 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.
KeywordMaxwell scattering problem PML equations Block triangular preconditioner Spectral distributions
DOI10.1016/j.camwa.2017.07.026
Language英语
Funding ProjectHi-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 Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000418980800015
PublisherPERGAMON-ELSEVIER SCIENCE LTD
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/27068
Collection中国科学院数学与系统科学研究院
Corresponding AuthorZou, Jun
Affiliation1.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
Recommended Citation
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.
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