A low-frequency fast multipole boundary element method based on analytical integration of the hypersingular integral for 3D acoustic problems

Wu, Haijun; Liu, Yijun; Jiang, Weikang

doi:10.1016/j.enganabound.2012.09.011

Cited by 26 publications

(9 citation statements)

References 44 publications

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“…The approach reported in this paper differs from those in in that it arises specifically from the wave nature of the fields involved. In particular, it draws on formulations derived for modelling aperture scattering, so has a specific physical interpretation.…”

Section: Introductionmentioning

confidence: 91%

“…The starting point for this is a surface integral identical to (12), so long as e j is defined to be piecewise-constant according to (10). In this analogy, o j is regarded as being the incident wave arriving at the screen, S j the aperture in the screen, and ‰ j the wave emerging from it on the other side.…”

Section: Finding a Contour Integral Kernelmentioning

confidence: 99%

“…An early and influential exposition of this approach was given by Terai [9], based on conversion to polar coordinates; this included support for higher-order polynomial basis functions, but was restricted to planar elements. More recently, there has been interest in evaluating the resulting line integrals analytically using a power series expansion [10], but this is valid only for piecewise-constant basis functions on planar polygonal elements.…”

Section: Introductionmentioning

confidence: 99%

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A transformation approach for efficient evaluation of oscillatory surface integrals arising in three‐dimensional boundary element methods

Hargreaves

Lam

Langdon

2016

Numerical Meth Engineering

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SUMMARYWe propose a method for efficient evaluation of surface integrals arising in boundary element methods for three-dimensional Helmholtz problems (with real positive wavenumber k/, modelling wave scattering and/or radiation in homogeneous media. To reduce the number of degrees of freedom required when k is large, a common approach is to include in the approximation space oscillatory basis functions, with support extending across many wavelengths. A difficulty with this approach is that it leads to highly oscillatory surface integrals whose evaluation by standard quadrature would require at least O k 2 quadrature points. Here, we use equivalent contour integrals developed for aperture scattering in optics to reduce this requirement to O .k/, and possible extensions to reduce it further to O .1/ are identified. The contour integral is derived for arbitrary shaped elements, but its application is limited to planar elements in many cases. In addition, the transform regularises the singularity in the surface integrand caused by the Green's function, including for the hyper-singular case under appropriate conditions. An open-source Matlab™code library is available to demonstrate our routines.

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Section: Introductionmentioning

confidence: 91%

Section: Finding a Contour Integral Kernelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A transformation approach for efficient evaluation of oscillatory surface integrals arising in three‐dimensional boundary element methods

Hargreaves

Lam

Langdon

2016

Numerical Meth Engineering

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“…The pulsating sphere is usually used in the literature as a simple example to show the effect of fictitious eigenfrequencies, see for example Refs. [44][45][46][47][48][49][50][51]. Before the numerical analysis of its fictitious eigenfrequencies using the present boundary element eigensolvers, the sound pressure at a position outside the sphere is also calculated to show the effect of fictitious eigenfrequencies.…”

Section: The Interior Of the Unit Spherementioning

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 acoustic Boundary Element Method has been applied to solve acoustic radiation and scattering problem in the exterior and interior closed domain for long time [2,4]. However, the traditional BEM has difficulty in solving the problem of thin body as the meshes on two sides are quite close.…”

Section: Introductionmentioning

confidence: 99%

Acoustic Scattering Performance of a Duct for a Monopole Source Using Thin-Body BEM Method

Yan¹,

Huang²,

Yi³

et al. 2016

Proceedings of the 2016 International Conference on Computer Engineering, Information Science &Amp; Application Technology (ICC

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In this paper, in order to calculate the acoustic scattering of the duct, a thin-body boundary element method (BEM) has been proposed and the velocity obtained by the acoustic velocity formulation is use1d as the Neumann boundary condition on a rigid scattering surface. The radiated sound pressure and the scattering effect of the solid wall on the propagation of the sound wave are calculated by using the Kirchhoff formulation and the thin-body BEM, respectively. Computational results for a monopole source verify the method. The sound pressure directivity and scattering effect are shown to demonstrate the applicability and validity of the approach.

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A low-frequency fast multipole boundary element method based on analytical integration of the hypersingular integral for 3D acoustic problems

Cited by 26 publications

References 44 publications

A transformation approach for efficient evaluation of oscillatory surface integrals arising in three‐dimensional boundary element methods

A transformation approach for efficient evaluation of oscillatory surface integrals arising in three‐dimensional boundary element methods

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

Acoustic Scattering Performance of a Duct for a Monopole Source Using Thin-Body BEM Method

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