legendre spectral galerkin method for electromagnetic scattering from large cavities

ISCAS OpenIR

	legendre spectral galerkin method for electromagnetic scattering from large cavities
	Li Huiyuan; Ma Heping; Sun Weiwei
	2013
发表期刊	SIAM Journal on Numerical Analysis
ISSN	0036-1429
卷号	51 期号:1 页码:353-376
摘要	The paper is concerned with the electromagnetic scattering from a large cavity embedded in an infinite ground plane, which is governed by a Helmholtz type equation with nonlocal hypersingular transparent boundary condition on the aperture. We first present some stability estimates with the explicit dependency of wavenumber for the Helmholtz type cavity problem. Then a Legendre spectral Galerkin method is proposed, in which the Legendre-Gauss interpolatory approximation is applicable to the hypersingular integral and a Legendre-Galerkin scheme is used for the approximation to the Helmholtz equation. The existence and the uniqueness of the approximation solution are established for large wavenumbers; the stability and the spectral convergence of the numerical method are then proved. Illustrative numerical results presented confirm our theoretical estimates and show that the proposed spectral method, compared with low-order finite difference methods, is especially effective for problems with large wavenumbers. © 2013 Society for Industrial and Applied Mathematics.; The paper is concerned with the electromagnetic scattering from a large cavity embedded in an infinite ground plane, which is governed by a Helmholtz type equation with nonlocal hypersingular transparent boundary condition on the aperture. We first present some stability estimates with the explicit dependency of wavenumber for the Helmholtz type cavity problem. Then a Legendre spectral Galerkin method is proposed, in which the Legendre-Gauss interpolatory approximation is applicable to the hypersingular integral and a Legendre-Galerkin scheme is used for the approximation to the Helmholtz equation. The existence and the uniqueness of the approximation solution are established for large wavenumbers; the stability and the spectral convergence of the numerical method are then proved. Illustrative numerical results presented confirm our theoretical estimates and show that the proposed spectral method, compared with low-order finite difference methods, is especially effective for problems with large wavenumbers. © 2013 Society for Industrial and Applied Mathematics.
收录类别	EI
关键词	Boundary Conditions Error Analysis Estimation Galerkin Methods Helmholtz Equation
部门归属	(1) Institute of Software Chinese Academy of Sciences Beijing 100190 China; (2) Department of Mathematics Shanghai University Shanghai 200444 China; (3) Department of Mathematics City University of Hong Kong Kowloon Hong Kong
语种	英语
WOS记录号	WOS:000315573700017
引用统计	被引频次：24[WOS] [WOS记录] [WOS相关记录]
内容类型	期刊论文
URI标识	http://ir.iscas.ac.cn/handle/311060/15644
专题	中国科学院软件研究所
推荐引用方式 GB/T 7714	Li Huiyuan,Ma Heping,Sun Weiwei. legendre spectral galerkin method for electromagnetic scattering from large cavities[J]. SIAM Journal on Numerical Analysis,2013,51(1):353-376.
APA	Li Huiyuan,Ma Heping,&Sun Weiwei.(2013).legendre spectral galerkin method for electromagnetic scattering from large cavities.SIAM Journal on Numerical Analysis,51(1),353-376.
MLA	Li Huiyuan,et al."legendre spectral galerkin method for electromagnetic scattering from large cavities".SIAM Journal on Numerical Analysis 51.1(2013):353-376.