The Adaptive Perfectly Matched Layer Method for Time-harmonic Acoustic and Electromagnetic Scattering Problems

Abstract. The recently introduced perfectly matched layer (PML) method is an efficient method to reduce the exterior wave propagation problem which is defined in the unbounded domain to the problem in the bounded domain. Under the assumption that the exterior solution is composed of outgoing waves only, the basic idea of the PML technique is to surround the computational domain by a layer of finite thickness with specially designed model medium that would attenuate all the waves that propagate from inside the computational domain. We report our recent efforts in developing the adaptive PML method for solving the time-harmonic acoustic and electromagnetic wave scattering problems. The method uses the a posteriori error estimate to determine the PML parameters such as the thickness of the layer and the artificial medium property. Combined with the adaptive finite element method, the adaptive PML method provides a complete numerical strategy to solve the scattering problems in the framework of finite element which produces automatically a coarse mesh size away from the fixed domain and thus makes the total computational costs insensitive to the thickness of the PML absorbing layer. We will consider the adaptive uniaxial PML method for the Helmholtz scattering problems in stratified medium and the electromagnetic scattering problems.