Quantification of Numerical Damping in the Acoustic Boundary Element Method for Two-Dimensional Duct Problems

Baydoun, Suhaib Koji; Marburg, Steffen

doi:10.1142/s2591728518500226

Cited by 13 publications

(13 citation statements)

References 25 publications

(27 reference statements)

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“…It is considered that real eigenvaulues are shifted into the complex plane following discretisation. This phenomenon is termed numerical damping [116][117][118][119].…”

Section: The Boundary Element Methods For the Generalised Boundary Conmentioning

confidence: 99%

The Boundary Element Method in Acoustics: A Survey

Kirkup

2019

Applied Sciences

106

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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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“…It is considered that real eigenvaulues are shifted into the complex plane following discretisation. This phenomenon is termed numerical damping [116][117][118][119].…”

Section: The Boundary Element Methods For the Generalised Boundary Conmentioning

confidence: 99%

The Boundary Element Method in Acoustics: A Survey

Kirkup

2019

Applied Sciences

106

View full text Add to dashboard Cite

show abstract

“…for x ∈ Ω j . Here, G j denotes the Green's function with the wavenumber of the respective region, that is, G j (x, y) = e k j |x−y| 4 |x − y| for x, y ∈ Ω j and x ≠ y (8) for j = 0, 1, 2, … , where denotes the complex unit. The boundary integral operators that map from one interface Γ n to another or the same interface Γ m are given by…”

Section: Boundary Integral Operatorsmentioning

confidence: 99%

Benchmarking preconditioned boundary integral formulations for acoustics

Wout

Haqshenas

Gélat

et al. 2021

Numerical Meth Engineering

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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 discretization 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 optimized 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.

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“…This problem is often used in the computational acoustics community for benchmarking purposes 43 and extensive studies on associated discretization errors with respect to mesh sizes and element types are available in the literature. 44,45 The acoustic field is discretized using a uniform mesh of 1120 quadrilateral boundary elements with bilinear discontinuous sound pressure interpolation yielding 4480 degrees of freedom. We are interested in solving the resultant linear system (2) in the frequency range from 40 to 210 Hz with frequency steps of Δf = 1 Hz, ie, m = 171.…”

Section: Plane Sound Wave In a Closed Rigid Ductmentioning

confidence: 99%

“…The system is free of dissipation, and hence, resonances occur at the integer multiples of 50 Hz. This problem is often used in the computational acoustics community for benchmarking purposes and extensive studies on associated discretization errors with respect to mesh sizes and element types are available in the literature …”

Section: Numerical Examplesmentioning

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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Quantification of Numerical Damping in the Acoustic Boundary Element Method for Two-Dimensional Duct Problems

Cited by 13 publications

References 25 publications

The Boundary Element Method in Acoustics: A Survey

The Boundary Element Method in Acoustics: A Survey

Benchmarking preconditioned boundary integral formulations for acoustics

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

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