Fast boundary integral method for acoustic wave scattering in two-dimensional layered media

TL;DR

This paper introduces a fast, scalable boundary integral method accelerated by FMM for efficiently solving acoustic wave scattering problems in layered two-dimensional media, handling complex geometries and multiple scatterers.

Contribution

The paper develops a layered-medium Green's function-based boundary integral approach combined with FMM acceleration, reducing computational complexity and enabling efficient simulations in complex layered media.

Findings

Achieves O(N) complexity in low frequency regimes

Validates accuracy and robustness through numerical experiments

Handles complex geometries and multiple scatterers effectively

Abstract

In this paper, we present a fast boundary integral method accelerated by the fast multipole method (FMM) for acoustic wave scattering governed by the scalar Helmholtz equation in multi-layered two-dimensional media. Multiple scatterers are randomly distributed in the multi-layered medium with some scatterers possibly intersecting layer interfaces. The boundary integral formulation employs a layered-medium Green's function to enforce transmission conditions across interfaces, thus avoiding unknowns on the interfaces and significantly reducing the size of the discretized problem compared to approaches that use a free-space Green's function. To demonstrate the FMM speedup, a low-order Nystr\"{o}m method is used to discretize the boundary integral equation and then the resulting dense linear system is solved by GMRES iterative solver accelerated by an improved layered media FMM and a overlapping domain decomposition preconditioning. In the low frequency regime, the proposed algorithm achieves an $\mathcal O(N)$ complexity. Numerical results validate the accuracy, efficiency and robustness of the method under complex settings and various incident angles. The proposed framework provides a scalable and efficient solver for acoustic wave scattering in layered media.