PML Method for Electromagnetic Scattering Problem in a Two-Layer Medium

The perfectly matched layer (PML) method is well-studied for acoustic scattering problems, electromagnetic scattering problems, and more recently, elastic scattering problems, with homogeneous background media. The purpose of this paper is to present the stability and exponential convergence of the PML method for three-dimensional electromagnetic scattering problem in a twolayer medium. The main contributions of this paper are threefold. Firstly, we establish the wellposedness of the original scattering problem for any Dirichlet boundary value in H(Div,ΓD) where ΓD stands for the boundary of the scatterer. Secondly, we propose a new weak formulation for the original problem where the Dirichlet-to-Neumann operator is proposed on a truncation boundary inside PML. This argument is favorable to the analysis for the PML Dirichlet-to-Neumann operator. The inf-sup condition is proved for the bilinear form. Thirdly, we establish the well-posedness of the PML problem and prove that the approximate solution converges to the original scattering solution exponentially as either the PML absorbing coefficient or the thickness of the PML increases.