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A plane wave method combined with local spectral elements for nonhomogeneous Helmholtz equation and time-harmonic Maxwell equations
Hu, Qiya1,3; Yuan, Long2
2018-02-01
Source PublicationADVANCES IN COMPUTATIONAL MATHEMATICS
ISSN1019-7168
Volume44Issue:1Pages:245-275
AbstractIn this paper we are concerned with plane wave discretizations of nonhomogeneous Helmholtz equation and time-harmonic Maxwell equations. To this end, we design a plane wave method combined with local spectral elements for the discretization of such nonhomogeneous equations. This method contains two steps: we first solve a series of nonhomogeneous local problems on auxiliary smooth subdomains by the spectral element method, and then apply the plane wave method to the discretization of the resulting (locally homogeneous) residue problem on the global solution domain. We derive error estimates of the approximate solutions generated by this method. The numerical results show that the resulting approximate solutions possess high accuracy.
KeywordHelmholtz equation Time-harmonic Maxwell equations Nonhomogeneous Local spectral element Plane wave basis functions Error estimates
DOI10.1007/s10444-017-9542-z
Language英语
Funding ProjectNatural Science Foundation of China[G11571352] ; China NSF[11501529] ; Qingdao applied basic research project[17-1-1-9-jch]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000423693000010
PublisherSPRINGER
Citation statistics
Cited Times:17[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/29409
Collection计算数学与科学工程计算研究所
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Scient Engn Comp, LSEC, Beijing 100190, Peoples R China
2.Shan Dong Univ Sci & Technol, Coll Math & Syst Sci, 579 Qian Wan Gang Rd, Qingdao 266590, Peoples R China
3.Univ Chinese Acad Sci, Beijing, Peoples R China
Recommended Citation
GB/T 7714
Hu, Qiya,Yuan, Long. A plane wave method combined with local spectral elements for nonhomogeneous Helmholtz equation and time-harmonic Maxwell equations[J]. ADVANCES IN COMPUTATIONAL MATHEMATICS,2018,44(1):245-275.
APA Hu, Qiya,&Yuan, Long.(2018).A plane wave method combined with local spectral elements for nonhomogeneous Helmholtz equation and time-harmonic Maxwell equations.ADVANCES IN COMPUTATIONAL MATHEMATICS,44(1),245-275.
MLA Hu, Qiya,et al."A plane wave method combined with local spectral elements for nonhomogeneous Helmholtz equation and time-harmonic Maxwell equations".ADVANCES IN COMPUTATIONAL MATHEMATICS 44.1(2018):245-275.
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