Solving Helmholtz equation at high wave numbers in exterior domains

doi:10.1016/j.amc.2016.11.015

	Solving Helmholtz equation at high wave numbers in exterior domains
	Wang, Kun 1,2; Wong, Yau Shu 2; Huang, Jizu3
	2017-04-01
发表期刊	APPLIED MATHEMATICS AND COMPUTATION
ISSN	0096-3003
卷号	298 页码:221-235
摘要	This paper presents effective difference schemes for solving the Helmholtz equation at high wave numbers. Considering the problems in the polar and spherical coordinates, we show that pollution-free difference schemes can be constructed for annulus and hollow sphere domains, but the "pollution effect" cannot be avoided in the neighborhood of the origin of the coordinate. Using the fact that the "pollution effect" appears in a small neighborhood of the origin of the coordinate, we propose a local mesh refinement approach so that a fine grid is applied only for a small region near the origin of the coordinate and a much larger grid size is employed in the remaining domain. The most attractive feature of this approach is that the computational storage can be significantly reduced while keeping almost the same numerical accuracy. Moreover, by applying a two-level local refinement technique, we can further enhance the performance of the proposed scheme. Numerical simulations are reported to verify the effectiveness of the proposed schemes for the Helmholtz problem in exterior domains. (C) 2016 Elsevier Inc. All rights reserved.
关键词	Helmholtz equation High wave number Local refinement Polar and spherical coordinates Pollution-free scheme
DOI	10.1016/j.amc.2016.11.015
语种	英语
资助项目	Natural Sciences and Engineering Research Council of Canada ; National Natural Science Foundation of China[11201506] ; National Natural Science Foundation of China[11501554] ; National Natural Science Foundation of China[11471312] ; Fundamental Research Funds for the Central Universities[106112015CDJXY100007]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000392785400017
出版者	ELSEVIER SCIENCE INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/24669
专题	计算数学与科学工程计算研究所
通讯作者	Wang, Kun
作者单位	1.Chongqing Univ, Coll Math & Stat, Chongqing 401331, Peoples R China 2.Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, NCMIS,LSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Wang, Kun,Wong, Yau Shu,Huang, Jizu. Solving Helmholtz equation at high wave numbers in exterior domains[J]. APPLIED MATHEMATICS AND COMPUTATION,2017,298:221-235.
APA	Wang, Kun,Wong, Yau Shu,&Huang, Jizu.(2017).Solving Helmholtz equation at high wave numbers in exterior domains.APPLIED MATHEMATICS AND COMPUTATION,298,221-235.
MLA	Wang, Kun,et al."Solving Helmholtz equation at high wave numbers in exterior domains".APPLIED MATHEMATICS AND COMPUTATION 298(2017):221-235.