Generalized plane wave discontinuous Galerkin methods for nonhomogeneous Helmholtz equations with variable wave numbers

doi:10.1080/00207160.2019.1616177

	Generalized plane wave discontinuous Galerkin methods for nonhomogeneous Helmholtz equations with variable wave numbers
	Yuan, Long 1; Hu, Qiya2,3
	2019-05-17
发表期刊	INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
ISSN	0020-7160
页码	22
摘要	In this paper we are concerned with numerical method for nonhomogeneous Helmholtz equations with variable wave numbers. We derive generalized plane wave basis functions for three-dimensional homogeneous Helmholtz equations with variable wave numbers. Then, by combining the local spectral element method, we design a generalized plane wave discontinuous Galerkin method for the discretization of such nonhomogeneous Helmholtz equations (in both dimensions two and three dimensions). We show that the approximation solutions generated by the proposed discretization method yield error estimates with high accuracies. Numerical results indicate that the resulting approximate solutions generated by the new method possess high accuracy and verify the validity of the theoretical results.
关键词	Helmholtz equation nonhomogeneous variable wave numbers generalized plane wave local spectral elements error estimates
DOI	10.1080/00207160.2019.1616177
语种	英语
资助项目	Natural Science Foundation of China -NSF[11501529] ; Scientific Research Foundation of Shandong University of Science and Technology for Recruited Talents ; Natural Science Foundation of China[G11571352] ; Qinddao applied basic research project[17-1-1-9-jch]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000470453000001
出版者	TAYLOR & FRANCIS LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/34875
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.Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao, Shandong, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Yuan, Long,Hu, Qiya. Generalized plane wave discontinuous Galerkin methods for nonhomogeneous Helmholtz equations with variable wave numbers[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS,2019:22.
APA	Yuan, Long,&Hu, Qiya.(2019).Generalized plane wave discontinuous Galerkin methods for nonhomogeneous Helmholtz equations with variable wave numbers.INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS,22.
MLA	Yuan, Long,et al."Generalized plane wave discontinuous Galerkin methods for nonhomogeneous Helmholtz equations with variable wave numbers".INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS (2019):22.