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A Two-Steps Method Based on Plane Wave for Nonhomogeneous Helmholtz Equations in Inhomogeneous Media
Hu, Qiya1,2; Zhao, Lin3
2018-08-01
Source PublicationNUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS
ISSN1004-8979
Volume11Issue:3Pages:453-476
AbstractIn this paper we are concerned with numerical methods for nonhomogeneous Helmholtz equations in inhomogeneous media. We try to extend the plane wave method, which has been widely used to the discretization of homogeneous Helmholtz equations with constant wave numbers, to solving nonhomogeneous Helmholtz equations with piecewise constant wave numbers. To this end, we propose a combination between the plane wave discontinuous Galerkin (PWDG) method and the high order element discontinuous Galerkin (HODG) method for the underlying Helmholtz equations. In this composite methods, we need only to solve a series of local Helmholtz equations by the HODG method and solve a locally homogeneous Helmholtz equation with element-wise constant wave number by the PWDG method. In particular, we first consider non-matching grids so that the generated approximations have better performance for the current case. Numerical experiments show that the proposed methods are very effective to the tested Helmholtz equations.
KeywordNonhomogeneous Helmholtz equation inhomogeneous media plane wave method discontinuous Galerkin method errors preconditioner
DOI10.4208/nmtma.2017-OA-0054
Language英语
Funding ProjectNatural Science Foundation of China[G11571352]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000438883300003
PublisherGLOBAL SCIENCE PRESS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/30801
Collection计算数学与科学工程计算研究所
Affiliation1.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
3.China Elect Corp, Huada Empyrean Software Co Ltd, Beijing, Peoples R China
Recommended Citation
GB/T 7714
Hu, Qiya,Zhao, Lin. A Two-Steps Method Based on Plane Wave for Nonhomogeneous Helmholtz Equations in Inhomogeneous Media[J]. NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS,2018,11(3):453-476.
APA Hu, Qiya,&Zhao, Lin.(2018).A Two-Steps Method Based on Plane Wave for Nonhomogeneous Helmholtz Equations in Inhomogeneous Media.NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS,11(3),453-476.
MLA Hu, Qiya,et al."A Two-Steps Method Based on Plane Wave for Nonhomogeneous Helmholtz Equations in Inhomogeneous Media".NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS 11.3(2018):453-476.
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