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 ANALYSIS OF POLLUTION-FREE APPROACHES FOR MULTI-DIMENSIONAL HELMHOLTZ EQUATIONS Wang, Kun1; Wong, Yau Shu2; Huang, Jizu3,4 2019 Source Publication INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING ISSN 1705-5105 Volume 16Issue:3Pages:412-435 Abstract Motivated by our recent work about pollution-free difference schemes for solving Helmholtz equation with high wave numbers, this paper presents an analysis of error estimate for the numerical solution on the annulus and hollow sphere domains. By applying the weighted-test-function method and defining two special interpolation operators, we first derive the existence, uniqueness, stability and the pollution-free error estimate for the one-dimensional problems generated from a method based on separation of variables. Utilizing the spherical harmonics and approximations results, we then prove the pollution-free error estimate in L-2-norm for multidimensional Helmholtz problems. Keyword Helmholtz equation error estimate finite difference method polar and spherical coordinates pollution-free scheme Language 英语 Funding Project National Natural Science Foundation of China[11501554] ; National Natural Science Foundation of China[91630205] ; Natural Sciences and Engineering Research Council of Canada ; Chongqing Research Program of Basic Research and Frontier Technology[cstc2017jcyjAX0231] ; Fundamental Research Funds for the Central Universities[106112017CDJXY100006] WOS Research Area Mathematics WOS Subject Mathematics, Applied ; Mathematics WOS ID WOS:000459446500003 Publisher ISCI-INST SCIENTIFIC COMPUTING & INFORMATION Citation statistics Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/32651 Collection 计算数学与科学工程计算研究所 Corresponding Author Wang, Kun Affiliation 1.Chongqing Univ, Coll Math & Stat, Chongqing 401331, Peoples R China2.Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China Recommended CitationGB/T 7714 Wang, Kun,Wong, Yau Shu,Huang, Jizu. ANALYSIS OF POLLUTION-FREE APPROACHES FOR MULTI-DIMENSIONAL HELMHOLTZ EQUATIONS[J]. INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING,2019,16(3):412-435. APA Wang, Kun,Wong, Yau Shu,&Huang, Jizu.(2019).ANALYSIS OF POLLUTION-FREE APPROACHES FOR MULTI-DIMENSIONAL HELMHOLTZ EQUATIONS.INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING,16(3),412-435. MLA Wang, Kun,et al."ANALYSIS OF POLLUTION-FREE APPROACHES FOR MULTI-DIMENSIONAL HELMHOLTZ EQUATIONS".INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING 16.3(2019):412-435.
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