Methods for Speeding Up the Boundary Element Solution of Acoustic Radiation Problems

Kirkup, Stephen Martin; Henwood, David

doi:10.1115/1.2930272

Cited by 18 publications

(19 citation statements)

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“…For example, for air-acoustics, the audible range for human being is up to 20 kHz and typically his could be resolved into components with a 10Hz resolution; multiplying the computational cost, considered in the previous Sub-subsection, by around 2000. The prospect of solving acoustic problems over the full frequency range has led to another set of techniques focus on reducing the computational burden by solving a range of frequencies together and these are usually termed multi-frequency methods [297,[348][349][350][351][352][353][354][355]. However, with the nature of an acoustic field, originating typically from structural vibration, is such that structural and acoustic resonances, and the driving profile, dominate the total acoustic response.…”

Section: The Frequency Factor Multi-frequency Methods and Wave Boundmentioning

confidence: 99%

The Boundary Element Method in Acoustics: A Survey

Kirkup

2019

Applied Sciences

101

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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.

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Section: The Frequency Factor Multi-frequency Methods and Wave Boundmentioning

confidence: 99%

The Boundary Element Method in Acoustics: A Survey

Kirkup

2019

Applied Sciences

101

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“…Another method for speeding up the multi-frequency computation was the so-called algebraic polynomial or the series expansion method (SEM) initially proposed by Kirkup et al 23 Recently, it has also been employed by Li 24 and Wang et al 25 in acoustic multi-frequency analysis. This approach separates the frequency-dependent terms from the integral kernels by means of the Taylor series expansion of the sine and cosine functions, making the numerical integration independent of frequency.…”

Section: Introductionmentioning

confidence: 99%

An Improved Series Expansion Method to Accelerate the Multi-Frequency Acoustic Radiation Prediction

Zhang

Mao

et al. 2015

J. Comp. Acous.

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Multi-frequency calculation is usually very time-consuming due to the repeated numerical integration for numerous frequencies in acoustic scattering or radiation problems. A series expansion method has been proposed to speed up this process just by taking the frequency-dependent terms out of the integral sign. However, this method, constrained by the number of truncation terms, is only applicable to low and medium frequencies and/or small-size structures. This paper develops an improved series expansion method that can be employed in a wider frequency band and larger-scale problems but with less computing expense. In the present method, the frequency-dependent term kr in the integral kernel is firstly transformed into the range from −π to π due to the periodicity of sine and cosine functions. Afterwards, truncation error would be kept reasonably small while the number of expansion terms would not increase with kr. Test cases of acoustic radiation from a pulsating sphere and a cat's eye structure are conducted and numerical results show significant reduction of computational time but suffering little accuracy loss for multi-frequency problems with this approach.

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“…Moreover, efficient procedures for the assembly of boundary element matrices in a frequency range have been developed. [19][20][21][22] Approximating the acoustic response itself can also be efficient in cases where only a small partition of the solution is of interest. 23,24 Furthermore, the high numerical complexity associated to fully populated boundary element matrices led to the development of several fast algorithms 25,26 that have also been combined with multifrequency strategies.…”

Section: Introductionmentioning

confidence: 99%

A greedy reduced basis scheme for multifrequency solution of structural acoustic systems

Baydoun

Voigt

Jelich

et al. 2019

Numerical Meth Engineering

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Summary The solution of frequency dependent linear systems arising from the discretization of vibro‐acoustic problems requires a significant computational effort in the case of rapidly varying responses. In this paper, we review the use of a greedy reduced basis scheme for the efficient solution in a frequency range. The reduced basis is spanned by responses of the system at certain frequencies that are chosen iteratively based on the response that is currently worst approximated in each step. The approximations at intermediate frequencies as well as the a posteriori estimations of associated errors are computed using a least squares solver. The proposed scheme is applied to the solution of an interior acoustic problem with boundary element method (BEM) and to the solution of coupled structural acoustic problems with finite element method and BEM. The computational times are compared to those of a conventional frequencywise strategy. The results illustrate the efficiency of the method.

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Methods for Speeding Up the Boundary Element Solution of Acoustic Radiation Problems

Cited by 18 publications

References 0 publications

The Boundary Element Method in Acoustics: A Survey

The Boundary Element Method in Acoustics: A Survey

An Improved Series Expansion Method to Accelerate the Multi-Frequency Acoustic Radiation Prediction

A greedy reduced basis scheme for multifrequency solution of structural acoustic systems

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