An FFT-accelerated PML-BIE Solver for Three-Dimensional Acoustic Wave Scattering in Layered Media

Abstract: This paper is concerned with three-dimensional acoustic wave scattering in two-layer media, where the two homogeneous layers are separated by a locally perturbed plane featuring an axially symmetric perturbation. A fast novel boundary integral equation (BIE) method is proposed to solve the scattering problem within a cylindrical perfectly matched layer (PML) truncation. We use PML-transformed Green's functions to derive BIEs in terms of single- and double-layer potentials for the wave field and its normal derivative on the boundary of each truncated homogeneous region. These BIEs, combined with interface and PML boundary conditions, form a complete system that accurately approximates the scattering problem. An FFT-based approach is introduced to efficiently and accurately discretize the surface integral operators in the BIEs, where a new kernel splitting technique is developed to resolve instabilities arising from the complex arguments in Green's functions. Numerical experiments demonstrate the efficiency and accuracy of the proposed method, as well as the exponential decay of truncation errors introduced by the PML.