A Two-Steps Method Based on Plane Wave for Nonhomogeneous Helmholtz Equations in Inhomogeneous Media

doi:10.4208/nmtma.2017-OA-0054

	A Two-Steps Method Based on Plane Wave for Nonhomogeneous Helmholtz Equations in Inhomogeneous Media
	Hu, Qiya1,2 ; Zhao, Lin 3
	2018-08-01
发表期刊	NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS
ISSN	1004-8979
卷号	11 期号:3 页码:453-476
摘要	In 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.
关键词	Nonhomogeneous Helmholtz equation inhomogeneous media plane wave method discontinuous Galerkin method errors preconditioner
DOI	10.4208/nmtma.2017-OA-0054
语种	英语
资助项目	Natural Science Foundation of China[G11571352]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000438883300003
出版者	GLOBAL SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/30801
专题	计算数学与科学工程计算研究所
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 3.China Elect Corp, Huada Empyrean Software Co Ltd, Beijing, Peoples R China
推荐引用方式 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.