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| legendre spectral galerkin method for electromagnetic scattering from large cavities | |
| Li Huiyuan; Ma Heping; Sun Weiwei | |
| 2013 | |
| Source | SIAM Journal on Numerical Analysis
 |
| ISSN | 0036-1429 |
| Volume | 51Issue:1Pages:353-376 |
| English Abstract | 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. |
| Indexed Type | EI |
| Keyword | Boundary Conditions Error Analysis Estimation Galerkin Methods Helmholtz Equation |
| Department | (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 |
| Language | 英语 |
| WOS ID | WOS:000315573700017 |
| Citation statistics | |
| Content Type | 期刊论文 |
| URI | http://ir.iscas.ac.cn/handle/311060/15644 |
| Collection | 中国科学院软件研究所 |
| Recommended Citation 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. |
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