Boundary integral formulations for acoustic modelling of high-contrast media

TL;DR

This paper develops specialized boundary integral formulations for acoustic scattering in high-contrast media, improving the conditioning and convergence of numerical solutions in such challenging scenarios.

Contribution

It introduces new boundary integral formulations tailored for high-contrast media, enhancing computational efficiency and stability in acoustic modeling.

Findings

Eigenvalues cluster away from zero, improving system conditioning.

Calderón preconditioning yields a single eigenvalue accumulation point.

Benchmark results show improved efficiency in high-contrast scattering simulations.

Abstract

The boundary element method is an efficient algorithm for simulating acoustic propagation through homogeneous objects embedded in free space. The conditioning of the system matrix strongly depends on physical parameters such as density, wavespeed and frequency. In particular, high contrast in density and wavespeed across a material interface leads to an ill-conditioned discretisation matrix. Therefore, the convergence of Krylov methods to solve the linear system is slow. Here, specialised boundary integral formulations are designed for the case of acoustic scattering at high-contrast media. The eigenvalues of the resulting system matrix accumulate at two points in the complex plane that depend on the density ratio and stay away from zero. The spectral analysis of the Calder\'on preconditioned PMCHWT formulation yields a single accumulation point. Benchmark simulations demonstrate the computational efficiency of the high-contrast Neumann formulation for scattering at high-contrast media.