A NOVEL LEAST SQUARES METHOD FOR HELMHOLTZ EQUATIONS WITH LARGE WAVE NUMBERS

doi:10.1137/19M1294101

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	A NOVEL LEAST SQUARES METHOD FOR HELMHOLTZ EQUATIONS WITH LARGE WAVE NUMBERS
	Hu, Qiya 1,2; Song, Rongrong 1,2
	2020
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	58 期号:5 页码:3091-3123
摘要	In this paper we are concerned with numerical methods for Helmholtz equations with large wave numbers. We design a least squares method for discretization of the considered Helmholtz equations. In this method, an auxiliary unknown is introduced on the common interface of any two neighboring elements and a quadratic objective functional is defined by the jumps of the traces of the solutions of local Helmholtz equations across all the common interfaces, where the local Helmholtz equations are defined on elements and are imposed Robin-type boundary conditions given by the auxiliary unknowns. A minimization problem with the objective functional is proposed to determine the auxiliary unknowns. The resulting discrete system of the auxiliary unknowns is Hermitian positive definite and so it can be solved by the preconditioned conjugate gradient method. Under some assumptions we show that the generated approximate solutions possess almost the same L-2 convergence order as the plane wave methods (for the case of constant wave number). Moreover, we construct a substructuring preconditioner for the discrete system of the auxiliary unknowns. Numerical experiments show that the proposed methods are very effective and have little "wave number pollution" for the tested Helmholtz equations with large wave numbers.
关键词	Helmholtz equations inhomogeneous media large wave number auxiliary unknowns least squares error estimates preconditioner
DOI	10.1137/19M1294101
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[G12071469]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000584721000027
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/52508
专题	中国科学院数学与系统科学研究院
通讯作者	Hu, Qiya
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Hu, Qiya,Song, Rongrong. A NOVEL LEAST SQUARES METHOD FOR HELMHOLTZ EQUATIONS WITH LARGE WAVE NUMBERS[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2020,58(5):3091-3123.
APA	Hu, Qiya,&Song, Rongrong.(2020).A NOVEL LEAST SQUARES METHOD FOR HELMHOLTZ EQUATIONS WITH LARGE WAVE NUMBERS.SIAM JOURNAL ON NUMERICAL ANALYSIS,58(5),3091-3123.
MLA	Hu, Qiya,et al."A NOVEL LEAST SQUARES METHOD FOR HELMHOLTZ EQUATIONS WITH LARGE WAVE NUMBERS".SIAM JOURNAL ON NUMERICAL ANALYSIS 58.5(2020):3091-3123.