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A FAST HIGH ORDER METHOD FOR electromagnetic SCATTERING BY LARGE OPEN CAVITIES

Journal of Computational Mathematics 2011年第3期29卷 287-304页

作者： Meiling Zhao Zhonghua Qiao Tao Tang School of Mathematics and System Science Beijing University of Aeronautics & Astronautics Beijing 100191 China Institute for Computational Mathematics & Department of Mathematics Hong Kong Baptist University Kowloon Hong Kong Department of Mathematics Hong Kong Baptist University Kowloon Hong Kong

In this paper, the electromagnetic scattering from a rectangular large open cavity embedded in an infinite ground plane is studied. By introducing a nonlocal artificial boundary condition, the scattering problem from the open cavity is reduced to a bounded domain problem. A compact fourth order finite difference scheme is then proposed to discrete the cavity scattering model in the rectangular domain, and a special treatment is enforced to approximate the boundary condition, which makes truncation errors reach （.9（h4） in the whole computational domain. A fast algorithm, exploiting the discrete Fourier transfor- mation in the horizontal and a Gaussian elimination in the vertical direction, is employed, which reduces the discrete system to a much smaller interface system. An effective pre- conditioner is presented for the BICGstab iterative solver to solve this interface system. Numerical results demonstrate the remarkable accuracy and efficiency of the proposed method. In particular, it can be used to solve the cavity model for the large wave number up to 600π.

关键词： electromagnetic cavity Compact finite difference scheme FFT Preconditioning.

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Analysis of Direct and Inverse cavity Scattering Problems

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Numerical Mathematics(Theory,Methods and Applications) 2011年第3期4卷 335-358页

作者： Gang Bao Jinglu Gao Peijun Li Department of Mathematics Zhejiang UniversityHangzhou 310027China. Department of Mathematics Michigan State UniversityEast LansingMI 48824USA. School of Mathematical Sciences Jilin UniversityChangchun 130023China. Department of Mathematics Purdue UniversityWest LafayetteIN 47907USA.

Consider the scattering of a time-harmonic electromagnetic plane wave by an arbitrarily shaped and filled cavity embedded in a perfect electrically conducting infinite ground plane.A method of symmetric coupling of finite element and boundary integral equations is presented for the solutions of electromagnetic scattering in both transverse electric and magnetic polarization *** the incident field,the direct problem is to determine the field distribution from the known shape of the cavity;while the inverse problem is to determine the shape of the cavity from the measurement of the field on an artificial boundary enclosing the *** this paper,both the direct and inverse scattering problems are discussed based on a symmetric coupling *** formulations for the direct scattering problem are presented,existence and uniqueness of weak solutions are studied,and the domain derivatives of the field with respect to the cavity shape are *** and local stability results are established in terms of the inverse problem.

关键词： electromagnetic cavity direct problem inverse problem finite element methods boundary integral equations.

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