The dual reciprocity boundary element method for the eigenvalue analysis of Helmholtz problems

Kontoni, D.P.N.

doi:10.1016/0965-9978(91)90002-j

Cited by 9 publications

(7 citation statements)

References 8 publications

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“…In this section, the dual reciprocity method (DRM) 29,45 and radial integration method (RIM) 46,47 are applied to the treatment of domain integral terms appearing in Equations ( 21) and ( 25), respectively.…”

Section: Approximation To the Domain Integrals And Discretizationmentioning

confidence: 99%

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Band structures analysis of fluid–solid phononic crystals using wavelet‐based boundary element method and frequency‐independent fundamental solutions

Wei

Xiang

Zhu

et al. 2023

Numerical Meth Engineering

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A novel method of combination of wavelet‐based boundary element method (WBEM) with frequency‐independent fundamental solutions is proposed to determine the band structures of fluid–solid phononic crystals (PCs) with square and triangular lattices. Integral equations established are based on the frequency‐independent fundamental solutions, which can avoid nonlinear eigenvalue problems and reduce computing time. Domain integral terms arising from the use of frequency‐independent fundamental solutions are handled with the radial integration method (RIM) and dual reciprocity method (DRM), respectively. The results show the lower precision in high frequency domain of using RIM to handle domain integral terms than that of using DRM, which can be solved by increasing Gauss point. The B‐spline wavelet on the interval and wavelet coefficients are applied to approximate the physical boundary conditions. It is proved that coupling conditions between matrix and scatterers and Bloch theorem are also applicable to wavelet coefficients. Some small matrix entries generated by wavelet vanishing moment characteristics are truncated by the provided matrix compression technique, and the influence of compressed matrices on the results is studied. Furthermore, the final Eigen equations constructed are modified to avoid numerical instability. Some examples are provided to demonstrate the accuracy and efficiency of the proposed method.

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Section: Approximation To the Domain Integrals And Discretizationmentioning

confidence: 99%

“…is the distance from the point P j where the function is applied to a point X, and the expression of ûj can be obtained via Equation (29) as 45 :…”

Section: Scalar Variable Problemmentioning

confidence: 99%

Band structures analysis of fluid–solid phononic crystals using wavelet‐based boundary element method and frequency‐independent fundamental solutions

Wei

Xiang

Zhu

et al. 2023

Numerical Meth Engineering

View full text Add to dashboard Cite

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“…Therefore, it is not an easy task to solve acoustic eigenproblems using BEM. In order to solve such problems, a number of transform methods have been proposed [11][12][13][14][15][16][17][18][19][20][21], including the dual reciprocity method [11,12], the particular integral method [13,14], the multiple reciprocity method [15] and their applications [16][17][18][19][20]. Also, a numerical eigenvalue analysis by the Galerkin BEM has been carried out in the framework of the concept of eigenproblems for holomorphic Fredholm operatorvalued functions [22].…”

Section: Introductionmentioning

confidence: 99%

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

Zheng

Chen

Gao

et al. 2015

Engineering Analysis with Boundary Elements

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“…The volume integrals caused by the non‐homogeneous term can be transformed into boundary integrals with the help of various methods, such as the dual reciprocity method , the particular integral method , the multiple reciprocity method , and the radial integration method . Further developments and applications of these volume‐ or domain‐integral transform methods can be found, e.g., in References for acoustic eigenvalue problems and in Reference for fluid–structure interaction eigenvalue problems.…”

Section: Introductionmentioning

confidence: 99%

“…The volume integrals caused by the non-homogeneous term can be transformed into boundary integrals with the help of various methods, such as the dual reciprocity method [23], the particular integral method [24], the multiple reciprocity method [25], and the radial integration method [26]. Further developments and applications of these volume-or domain-integral transform methods can be found, e.g., in References [27][28][29][30][31][32] for acoustic eigenvalue problems and in Reference [33] for fluid-structure interaction eigenvalue problems.Besides the methods mentioned earlier, contour integral methods [34][35][36][37][38] have been recently developed. By virtue of the contour integral methods presented in References [35][36][37][38], a nonlinear eigenvalue problem can be easily converted into a linear one whose dimension is much smaller than the original one.…”

mentioning

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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The dual reciprocity boundary element method for the eigenvalue analysis of Helmholtz problems

Cited by 9 publications

References 8 publications

Band structures analysis of fluid–solid phononic crystals using wavelet‐based boundary element method and frequency‐independent fundamental solutions

Band structures analysis of fluid–solid phononic crystals using wavelet‐based boundary element method and frequency‐independent fundamental solutions

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

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

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