Adaptive computation with PML for time-harmonic scattering problems

We introduce an adaptive perfectly matched layer (PML) technique for solving the time harmonic scattering problems. The PML parameters such as the thickness of the layer and the fictitious medium property are determined through sharp a posteriori error estimates. The derived finite element a posteriori estimate for adapting meshes has the nice feature that it decays exponentially away from the boundary of the fixed domain where the PML layer is placed. This property makes the total computational costs insensitive to the thickness of the PML absorbing layers. A numerical example is included to illustrate the competitive behavior of the proposed adaptive method.