Fast algorithms for the electromagnetic scattering by partly covered cavities

We study the electromagnetic scattering by the partly covered cavity with high wave numbers, which is governed by a Helmholtz equation with the transparent boundary condition. First, we develop a fast high-order algorithm for the scattering by the partly covered cavity filled with the homogeneous medium. The Helmholtz equation is discretized using a fourth-order finite-difference scheme and then reduced into a small aperture system by the fast Fourier transformation and Gaussian elimination. The existence and uniqueness of the numerical solution are given. By means of the immersed interface method, we also propose a fast high-order method for solving the scattering by the partly covered cavity with inhomogeneous media. A preconditioned iterative method based on Krylov subspace is applied to accelerate the convergence. Numerical experiments with different types of media are presented to demonstrate the efficiency and validity of the proposed methods.