Convergence of the Uniaxial Perfectly Matched Layer Method for Time-Harmonic Scattering Problems in Two-Layered Media

Abstract. In this paper, we propose a uniaxial perfectly matched layer (PML) method for solving the time-harmonic scattering problems in two-layered media. The exterior region of the scatterer is divided into two half spaces by an infinite plane, on two sides of which the wave number takes different values. We surround the computational domain where the scattering field is interested by a PML layer with the uniaxial medium property. By imposing homogenous boundary condition on the outer boundary of the PML layer, we show that the solution of the PML problem converges exponentially to the solution of the original scattering problem in the computational domain as either the PML absorbing coefficient or the thickness of the PML layer tends to infinity.