Is the Burton–Miller formulation really free of fictitious eigenfrequencies?

Zheng, Changjun; Chen, Haibo; Gao, Haifeng; Du, Lei

doi:10.1016/j.enganabound.2015.04.014

Cited by 85 publications

(41 citation statements)

References 49 publications

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“…16,22 Recent studies on BEM in exterior acoustics were published by Ramesh et al 23 and Marburg. 24,25 The method is also applied for eigenvalue analysis in the exterior acoustic problem by Zheng et al 26 The convergence of the infinite elements was shown by Demkowicz and Gerdes 27,28 and proves the reliability of the approach, but there have been no studies yet on the influence of the infinite elements on modes in exterior acoustics. This paper will first give an overview of the formulation of the infinite elements and of the suitability of the considered polynomials as radial interpolation functions.…”

Section: Introductionmentioning

confidence: 99%

Infinite Elements and Their Influence on Normal and Radiation Modes in Exterior Acoustics

Moheit

Marburg

2017

J. Comp. Acous.

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Acoustic radiation modes (ARMs) and normal modes (NMs) are calculated at the surface of a fluid-filled domain around a solid structure and inside the domain, respectively. In order to compute the exterior acoustic problem and modes, both the finite element method (FEM) and the infinite element method (IFEM) are applied. More accurate results can be obtained by using finer meshes in the FEM or higher-order radial interpolation polynomials in the IFEM, which causes additional degrees of freedom (DOF). As such, more computational cost is required. For this reason, knowledge about convergence behavior of the modes for different mesh cases is desirable, and is the aim of this paper. It is shown that the acoustic impedance matrix for the calculation of the radiation modes can be also constructed from the system matrices of finite and infinite elements instead of boundary element matrices, as is usually done. Grouping behavior of the eigenvalues of the radiation modes can be observed. Finally, both kinds of modes in exterior acoustics are compared in the example of the cross-section of a recorder in air. When the number of DOF is increased by using higher-order radial interpolation polynomials, different eigenvalue convergences can be observed for interpolation polynomials of even and odd order.

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Section: Introductionmentioning

confidence: 99%

Infinite Elements and Their Influence on Normal and Radiation Modes in Exterior Acoustics

Moheit

Marburg

2017

J. Comp. Acous.

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“…(18)- (19), and only the true eigenvalues are obtained. In BEM analysis, the recommended value of γ for a time factor e iωt is −i/k [39]. While the SBM can be understood as a strong-form collocation version of the indirect BEM [36], we also set γ = −i/k in this paper.…”

Section: The Burton-miller Methodsmentioning

confidence: 99%

“…According to new research [39], the Burton-Miller method is not really free of fictitious eigenvalues, but it can be viewed as a penalty method to some degree, and moves the fictitious eigenvalues into the complex plane. Therefore, it still can be used in numerical analysis for acoustic problems.…”

Section: The Burton-miller Methodsmentioning

confidence: 99%

Singular boundary method for acoustic eigenanalysis

Chen

Pang

2016

Computers & Mathematics with Applications

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a b s t r a c tThis paper applies the singular boundary method (SBM) to two-(2D) and threedimensional (3D) acoustics eigenproblems in simply-and multiply-connected domains. The SBM is a strong-form boundary discretization numerical method and is meshless, integration-free, and easy-to-implement. By introducing the concept of the source intensity factors, the singularity of fundamental solutions can be isolated to avoid the singular numerical integrals in the boundary element method (BEM). Similar to the BEM, the spurious eigenvalues may arise in the SBM computation. In order to extract out spurious eigenvalues from SBM results, the singular value decomposition updating techniques and the Burton-Miller method are implemented. Several 2D and 3D benchmark examples subjected to Dirichlet and Neumann boundaries are tested to examine the accuracy and stability of the present SBM strategy.

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“…In addition, the Burton–Miller method is applied to tackle the fictitious eigenfrequency problem of the conventional boundary integral equation method in solving exterior acoustic problems. In our previous work , the actual effect of the Burton–Miller formulation on tackling the fictitious eigenfrequency problem is investigated, and the optimal choice of the coupling parameter α as i/ k (where i is the imaginary unit and k is the wave number) is confirmed through exterior sphere examples, e.g., a pulsating sphere example. In this paper, further studies are conducted for the fluid–structure interaction problems and the optimal choice of the coupling parameter α as i/ k is further confirmed for the coupled FE–BE methods for the fluid–structure interaction analysis.…”

Section: Introductionmentioning

confidence: 99%

Coupled FE–BE method for eigenvalue analysis of elastic structures submerged in an infinite fluid domain

Zheng

Zhang

et al. 2016

Numerical Meth Engineering

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Summary For thin elastic structures submerged in heavy fluid, e.g., water, a strong interaction between the structural domain and the fluid domain occurs and significantly alters the eigenfrequencies. Therefore, the eigenanalysis of the fluid–structure interaction system is necessary. In this paper, a coupled finite element and boundary element (FE–BE) method is developed for the numerical eigenanalysis of the fluid–structure interaction problems. The structure is modeled by the finite element method. The compressibility of the fluid is taken into consideration, and hence the Helmholtz equation is employed as the governing equation and solved by the boundary element method (BEM). The resulting nonlinear eigenvalue problem is converted into a small linear one by applying a contour integral method. Adequate modifications are suggested to improve the efficiency of the contour integral method and avoid missing the eigenvalues of interest. The Burton–Miller formulation is applied to tackle the fictitious eigenfrequency problem of the BEM, and the optimal choice of its coupling parameter is investigated for the coupled FE–BE method. Numerical examples are given and discussed to demonstrate the effectiveness and accuracy of the developed FE–BE method. Copyright © 2016 John Wiley & Sons, Ltd.

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Is the Burton–Miller formulation really free of fictitious eigenfrequencies?

Cited by 85 publications

References 49 publications

Infinite Elements and Their Influence on Normal and Radiation Modes in Exterior Acoustics

Infinite Elements and Their Influence on Normal and Radiation Modes in Exterior Acoustics

Singular boundary method for acoustic eigenanalysis

Coupled FE–BE method for eigenvalue analysis of elastic structures submerged in an infinite fluid domain

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