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A Fast Preconditioned Iterative Algorithm for the Electromagnetic Scattering from a Large Cavity

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Abstract

In this paper, a fast preconditioned Krylov subspace iterative algorithm is proposed for the electromagnetic scattering from a rectangular large open cavity embedded in an infinite ground plane. The scattering problem is described by the Helmholtz equation with a nonlocal artificial boundary condition on the aperture of the cavity and Dirichlet boundary conditions on the walls of the cavity. Compact fourth order finite difference schemes are employed to discretize the bounded domain problem. A much smaller interface discrete system is reduced by introducing the discrete Fourier transformation in the horizontal and a Gaussian elimination in the vertical direction, presented in Bao and Sun (SIAM J. Sci. Comput. 27:553, 2005). An effective preconditioner is developed for the Krylov subspace iterative solver to solve this interface system. Numerical results demonstrate the remarkable efficiency and accuracy of the proposed method.

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Acknowledgements

The authors would like to thank the referees for their valuable suggestions. The authors would also like to thank Professor Tao Tang at Hong Kong Baptist University and Dr. Jari Toivanen at Stanford University for their beneficial discussions. The research of the first author was partially supported by NSFC (Nos. 11161014 and 11001062) and Guangxi Science and Technology Development Foundation (No. 0731018). The research of the second author was partially supported by the Hong Kong RGC grant (No. 201710).

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Authors and Affiliations

  1. Guilin University of Electronics Technology, Guilin, Guangxi, 541004, China

    Chenliang Li

  2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

    Zhonghua Qiao

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  1. Chenliang Li
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  2. Zhonghua Qiao
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Correspondence to Zhonghua Qiao.

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Li, C., Qiao, Z. A Fast Preconditioned Iterative Algorithm for the Electromagnetic Scattering from a Large Cavity. J Sci Comput 53, 435–450 (2012). https://doi.org/10.1007/s10915-012-9580-0

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  • DOI: https://doi.org/10.1007/s10915-012-9580-0

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