Perfectly matched layer boundary integral equation method for wave scattering in a layered medium

For scattering problems of time-harmonic waves, the boundary integral equation (BIE) methods are highly competitive since they are formulated on lower-dimension boundaries or interfaces and can automatically satisfy outgoing radiation conditions. For scattering problems in a layered medium, standard BIE methods based on Green's function of the background medium need to evaluate the expensive Sommerfeld integrals. Alternative BIE methods based on the freespace Green's function give rise to integral equations on unbounded interfaces which are not easy to truncate since the wave Fields on these interfaces decay very slowly. We develop a BIE method based on the perfectly matched layer (PML) technique. The PMLs are widely used to suppress outgoing waves in numerical methods that directly discretize the physical space. Our PML-based BIE method uses the PML-transformed free-space Green's function to deFine the boundary integral operators. The method is eficient since the PML-transformed free-space Green's function is easy to evaluate and the PMLs are very effective in truncating the unbounded interfaces. Numerical examples are presented to validate our method and demonstrate its accuracy.