Efficient integral equation solvers for layered-medium scattering problems

This paper revisits and outlines highly accurate boundary integral equation (BIE) solvers for solving the acoustic, elastic and electromagnetic layered-medium scattering problems, especially the windowed Green's function method (WGF) and the perfectly matched layer (PML)-based BIE method. Unlike standard approaches, neither of these two methods requires the use of layer Green's functions containing highly expensive Sommerfeld integrals. The WGF method derives an integral equation formulation based on the free-space Green's function (FGF), together with smooth operator windowing and a correction strategy. The PML-BIE method truncates the considered infinite domain using the PML and then results in BIEs on local defects in terms of PML-transformed FGF. Numerical examples are presented to validate these two methods and demonstrate their accuracy. Finally, some related open problems will also be provided.This article is part of the theme issue 'Analytically grounded full-wave methods for advances in computational electromagnetics'.