A highly accurate perfectly-matched-layer boundary integral equation solver for acoustic layered-medium problems

TL;DR

This paper introduces a high-accuracy boundary integral equation solver for acoustic scattering in layered media, utilizing PML and Chebyshev discretization to efficiently handle complex geometries in 2D and 3D.

Contribution

It develops a novel PML-based BIE solver with high-order discretization for layered-medium acoustic problems, improving accuracy and efficiency over existing methods.

Findings

Achieves high accuracy in 2D and 3D acoustic scattering simulations.

Demonstrates efficiency and robustness through numerical experiments.

Effectively handles complex layered geometries with defect regions.

Abstract

Based on the perfectly matched layer (PML) technique, this paper develops a high-accuracy boundary integral equation (BIE) solver for acoustic scattering problems in locally defected layered media in both two and three dimensions. The original scattering problem is truncated onto a bounded domain by the PML. Assuming the vanishing of the scattered field on the PML boundary, we derive BIEs on local defects only in terms of using PML-transformed free-space Green's function, and the four standard integral operators: single-layer, double-layer, transpose of double-layer, and hyper-singular boundary integral operators. The hyper-singular integral operator is transformed into a combination of weakly-singular integral operators and tangential derivatives. We develop a high-order Chebyshev-based rectangular-polar singular-integration solver to discretize all weakly-singular integrals. Numerical experiments for both two- and three-dimensional problems are carried out to demonstrate the accuracy and efficiency of the proposed solver.