The Boundary Element Method in Acoustics: A Survey

Abstract

The boundary element method (BEM) in the context of acoustics or Helmholtz problems is reviewed in this paper. The basis of the BEM is initially developed for Laplace’s equation. The boundary integral equation formulations for the standard interior and exterior acoustic problems are stated and the boundary element methods are derived through collocation. It is shown how interior modal analysis can be carried out via the boundary element method. Further extensions in the BEM in acoustics are also reviewed, including half-space problems and modelling the acoustic field surrounding thin screens. Current research in linking the boundary element method to other methods in order to solve coupled vibro-acoustic and aero-acoustic problems and methods for solving inverse problems via the BEM are surveyed. Applications of the BEM in each area of acoustics are referenced. The computational complexity of the problem is considered and methods for improving its general efficiency are reviewed. The significant maintenance issues of the standard exterior acoustic solution are considered, in particular the weighting parameter in combined formulations such as Burton and Miller’s equation. The commonality of the integral operators across formulations and hence the potential for development of a software library approach is emphasised.

Mapping Industry 4.0 Enabling Technologies into United Nations Sustainability Development Goals

“…the basis for simulating larger systems that creates I4.0. Simulation in this part includes Finite Element Analysis (FEA) [69], simulation of acoustics performance of the product [70,71] simulation of composites structures behavior and the progressive degradation [72,73] and fluid dynamics simulation [74] can be distinguished. One of process simulation challenges is the development of Computer Aided Manufacturing (CAM) to automate a manufacturing process [75].…”

Special Issue on Modelling, Simulation and Data Analysis in Acoustical Problems

“…An acoustic detection method for localization is proposed by Yin et al in [31]. Kirkup [32] proposes a survey of the boundary element method in acoustics. Sparse impulse response estimation is treated in [33] by Lim et al…”

A Pilot Fortran Software Library for the Solution of Laplace’s Equation by the Boundary Element Method

“…The focus of this work is the algorithms and the software for solving Laplace problems by the BEM. As with the earlier works by the first author on Laplace and Helmholtz (acoustic) problems [20][21][22][23][24], this is about continuing with the development of a base library of methods and corresponding software. The codes and guides can be found on the first author's website [25].…”