Two transparent boundary conditions for the electromagnetic scattering from two-dimensional overfilled cavities

Authors:
Kui Du
Affiliations:
School of Mathematical Sciences, Xiamen University, Xiamen 361005, China and Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong
Venue:
Journal of Computational Physics
Year:
2011

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Abstract

We consider electromagnetic scattering from two-dimensional (2D) overfilled cavities embedded in an infinite ground plane. The unbounded computational domain is truncated to a bounded one by using a transparent boundary condition (TBC) proposed on a semi-ellipse. For overfilled rectangular cavities with homogeneous media, another TBC is introduced on the cavity apertures, which produces a smaller computational domain. The existence and uniqueness of the solutions of the variational formulations for the transverse magnetic and transverse electric polarizations are established. In the exterior domain, the 2D scattering problem is solved in the elliptic coordinate system using the Mathieu functions. In the interior domain, the problem is solved by a finite element method. Numerical experiments show the efficiency and accuracy of the new boundary conditions.