Perfectly matched layer for scattering problems in homogeneous media


In this lecture, I will talk about the perfectly matched layer (PML) method for scattering problems in inhomogeneous materials, particularly, in layered media and half space with step-like surface. I will present a framework to analyze Green’s functions and the well-posedness of approximate problems with PML boundary conditions. For incident waves impinged on a step-like surface, the scattering problem is formulated into an interface problem. We propose a piecewise circular PML method to solve the scattering problem. Existence, uniqueness, and error estimates are proved for the PML solution.