Comparisons of three kinds of plane wave methods for the Helmholtz equation and time-harmonic Maxwell equations with complex wave numbers

doi:10.1016/j.cam.2018.05.024

	Comparisons of three kinds of plane wave methods for the Helmholtz equation and time-harmonic Maxwell equations with complex wave numbers
	Yuan, Long 1; Hu, Qiya2,3
	2018-12-15
发表期刊	JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN	0377-0427
卷号	344 页码:323-345
摘要	In 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.
关键词	Helmholtz equation Time-harmonic Maxwell's equations Well posedness Electromagnetic wave Plane wave basis Error estimates
DOI	10.1016/j.cam.2018.05.024
语种	英语
资助项目	China 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研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000440394900022
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/30765
专题	计算数学与科学工程计算研究所
通讯作者	Yuan, Long
作者单位	1.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
推荐引用方式 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.