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arXiv · 2511.12450

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

Linfeng Xia·Heng Yuan·Bo Wang·Wei Cai
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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.

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Linfeng Xia, Heng Yuan, Bo Wang, Wei Cai. 2025-11-16. Fast boundary integral method for acoustic wave scattering in two-dimensional layered media. https://arxiv.org/abs/2511.12450

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