A Second-Order Method for the Electromagnetic Scattering from a Large Cavity

In this paper, we study the electromagnetic scattering from a two dimen- sional large rectangular open cavity embedded in an infinite ground plane, which is modelled by Helmholtz equations. By introducing nonlocal transparent boundary con- ditions, the problem in the open cavity is reduced to a bounded domain problem. A hypersingular integral operator and a weakly singular integral operator are involved in the TM and TE cases, respectively. A new second-order Toeplitz type approximation and a second-order finite difference scheme are proposed for approximating the hyper- singular integral operator on the aperture and the Helmholtz in the cavity, respectively. The existence and uniqueness of the numerical solution in the TE case are established for arbitrary wavenumbers. A fast algorithm for the second-order approximation is pro- posed for solving the cavity model with layered media. Numerical results show the second-order accuracy and efficiency of the fast algorithm. More important is that the algorithm is easy to implement as a preconditioner for cavity models with more general media.

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