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 Generalized plane wave discontinuous Galerkin methods for nonhomogeneous Helmholtz equations with variable wave numbers Yuan, Long1; Hu, Qiya2,3 2019-05-17 Source Publication INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS ISSN 0020-7160 Pages 22 Abstract 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. Keyword Helmholtz equation nonhomogeneous variable wave numbers generalized plane wave local spectral elements error estimates DOI 10.1080/00207160.2019.1616177 Language 英语 Funding Project 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 Research Area Mathematics WOS Subject Mathematics, Applied WOS ID WOS:000470453000001 Publisher TAYLOR & FRANCIS LTD Citation statistics Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/34875 Collection 计算数学与科学工程计算研究所 Corresponding Author Hu, Qiya Affiliation 1.Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao, Shandong, Peoples R China2.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China Recommended CitationGB/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.
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