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Comparisons of three kinds of plane wave methods for the Helmholtz equation and time-harmonic Maxwell equations with complex wave numbers
Yuan, Long1; Hu, Qiya2,3
2018-12-15
Source PublicationJOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN0377-0427
Volume344Pages:323-345
AbstractIn this paper we are concerned with some plane wave discretization methods of the Helmholtz equation and time-harmonic Maxwell equations with complex wave numbers. We design two new variants of the variational theory of complex rays and the ultra weak variational formulation for the discretization of these types of equations, respectively. The well posedness of the approximate solutions generated by the two methods is derived. Moreover, based on the PWLS-LSFE method introduced in Hu and Yuan (2018), we extend these two methods (VTCR method and UWVF method) combined with local spectral element to discretize nonhomogeneous Helmholtz equation and Maxwell's equations. The numerical results show that the resulting approximate solution generated by the UWVF method is clearly more accurate than that generated by the VTCR method. (C) 2018 Elsevier B.V. All rights reserved.
KeywordHelmholtz equation Time-harmonic Maxwell's equations Well posedness Electromagnetic wave Plane wave basis Error estimates
DOI10.1016/j.cam.2018.05.024
Language英语
Funding ProjectChina NSF[11501529] ; Qinddao applied basic research project[17-1-1-9-jch] ; Scientific Research Foundation of Shandong University of Science and Technology for Recruited Talents ; Natural Science Foundation of China[G11571352]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000440394900022
PublisherELSEVIER SCIENCE BV
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/30765
Collection计算数学与科学工程计算研究所
Affiliation1.Shandong Univ Sci & Technol, Coll Math & Syst Sci, 579 Qian Wan Gang Rd, Qingdao 266590, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China
3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Yuan, Long,Hu, Qiya. Comparisons of three kinds of plane wave methods for the Helmholtz equation and time-harmonic Maxwell equations with complex wave numbers[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2018,344:323-345.
APA Yuan, Long,&Hu, Qiya.(2018).Comparisons of three kinds of plane wave methods for the Helmholtz equation and time-harmonic Maxwell equations with complex wave numbers.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,344,323-345.
MLA Yuan, Long,et al."Comparisons of three kinds of plane wave methods for the Helmholtz equation and time-harmonic Maxwell equations with complex wave numbers".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 344(2018):323-345.
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