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

Abstract

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 a three-dimensional electromagnetic scattering problem in a two-layer medium. The main contributions of this paper are threefold. First, we establish the well-posedness of the original scattering problem for any Dirichlet boundary value in $\boldsymbol{H}^{-1/2}({\rm Div},\Gamma_D),$ where $\Gamma_D$ stands for the boundary of the scatterer. Second, we propose a new weak formulation for the original problem, where the Dirichlet-to-Neumann operator is proposed on a truncation boundary inside the PML. This argument is favorable in the analysis of the PML Dirichlet-to-Neumann operator. The inf-sup condition is proved for the bilinear form. Third, we establish the well-posedness of the PML problem a...