A perfectly matched layer–boundary integral equation method for wave scattering in a two-layer medium of a step-like interface

This paper is concerned with wave scattering in a two-layer medium separated by a step-like interface, consisting of two half lines with different heights. For a plane-wave incidence, the two half lines generate parallel reflected and transmitted plane waves of different phases, posing a challenge in identifying the radiation behaviour of the scattered field at infinity. To tackle this difficulty, we introduce a transition curve that connects the reflection and transmission directions to divide the space into two unbounded regions. We propose that subtracting the corresponding plane waves from the scattered field in either region yields a piecewise-defined outgoing wave that satisfies the Sommerfeld radiation condition. We adopt a uniaxial perfectly matched layer (PML) to truncate the outgoing wave. Within each of the four bounded regions separated by the transition curve, the interface and the PML boundary, we use the PML-transformed Green's function to derive a boundary integral equation (BIE). A high-accuracy quadrature is adopted to discretize the four BIEs. Together with the interface conditions, they yield a final linear system with unknowns approximating the outgoing wave. Several numerical experiments are carried out to illustrate the validity of the radiation condition and the accuracy of the proposed solver.This article is part of the theme issue 'Analytically grounded full-wave methods for advances in computational electromagnetics'.