Benchmarking preconditioned boundary integral formulations for acoustics

TL;DR

This paper benchmarks various preconditioned boundary integral formulations for acoustic wave simulations, providing insights into their computational efficiency and robustness across diverse geometries and configurations.

Contribution

It offers a comprehensive survey and extensive benchmarking of boundary integral formulations and preconditioners for acoustics, aiding optimal method selection.

Findings

Preconditioned formulations significantly reduce computational time.

Certain formulations outperform others depending on geometry and frequency.

Extensive benchmarks reveal the strengths and limitations of various models.

Abstract

The boundary element method (BEM) is an efficient numerical method for simulating harmonic wave propagation. It uses boundary integral formulations of the Helmholtz equation at the interfaces of piecewise homogeneous domains. The discretisation of its weak formulation leads to a dense system of linear equations, which is typically solved with an iterative linear method such as GMRES. The application of BEM to simulating wave propagation through large-scale geometries is only feasible when compression and preconditioning techniques reduce the computational footprint. Furthermore, many different boundary integral equations exist that solve the same boundary value problem. The choice of preconditioner and boundary integral formulation is often optimised for a specific configuration, depending on the geometry, material characteristics, and driving frequency. On the one hand, the design flexibility for the BEM can lead to fast and accurate schemes. On the other hand, efficient and robust algorithms are difficult to achieve without expert knowledge of the BEM intricacies. This study surveys the design of boundary integral formulations for acoustics and their acceleration with operator preconditioners. Extensive benchmarks provide valuable information on the computational characteristics of several hundred different models for multiple reflection and transmission of acoustic waves.