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.
Highlights
Acoustics is the science of sound and has particular applications in sound reproduction, noise and sensing [1,2]
The main purpose of this paper is to encapsulate the modern scope of the boundary element method in acoustics; how it can be adopted for general 2D, 3D and axisymmetric dimensions, interior, exterior and half-space problems, thin shells and modal analysis
The standard boundary element method (BEM) can be directly applied to an enclosed domain with cavities or to multi-boundary problems in an exterior domain
Summary
Acoustics is the science of sound and has particular applications in sound reproduction, noise and sensing [1,2]. Numerical methods are only useful in practice when they are implemented on computer. It is over the last sixty years or so that numerical methods have become increasingly developed and computers have become faster, with increasing data storage and more widespread. This brings us to the wide-ranging area of computational acoustics; the solution of acoustic problems on computer [6,7,8,9,10,11], which has significantly developed in this timescale
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