Boundary integral equations for thin bodies

Krishnasamy, G.; Rizzo, F. J.; Liu, Yijun

doi:10.1002/nme.1620370108

Cited by 88 publications

(57 citation statements)

References 15 publications

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“…Special solution strategies can be adopted that avoid this problem. The so-called dual BEM formulation is one such strategy (as reported in Portela et al [8], Chen and Hong [9] and Krishnasamy et al [10]): in it, both the classic boundary integral equation and its first spatial derivative along the orthogonal direction to the boundary are used to obtain a non-singular system of equations. If the thickness of the obstacle is null a very effective Traction-BEM (TBEM) formulation can also be used (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Sound pressure attenuation provided by a 3D rigid acoustic barrier on a building façade: the influence of its longitudinal shape

Tadeu¹,

António²,

Castro³

2012

WIT Transactions on Modelling and Simulation

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This paper models the propagation of sound in the vicinity of 3D acoustic barriers placed parallel to a building façade to mitigate the noise generated by point pressure sources. The barriers are assumed to be very thin rigid elements. The problem is solved by developing and implementing a 3D boundary element method formulation based on the normal derivative integral equation (TBEM). The TBEM is formulated in the frequency domain and the resulting hypersingular terms are computed analytically. After verifying the model against 2.5D BEM solutions, several numerical applications are described to illustrate the practical usefulness of the proposed approaches. Different longitudinal barrier geometries are simulated to evaluate the influence of this characteristic on the sound pressure level attenuation attained at the building façade. Keywords: acoustic wave propagation, 3D thin barriers, normal derivative integral equation, analytical integration of hypersingular integrals.

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Section: Introductionmentioning

confidence: 99%

Sound pressure attenuation provided by a 3D rigid acoustic barrier on a building façade: the influence of its longitudinal shape

Tadeu¹,

António²,

Castro³

2012

WIT Transactions on Modelling and Simulation

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“…Huang and Cruse (1993) presented another approach taking a coordinate transformation to relax nearly singular kernels. Other approaches include Gaussian integration with fine subdivisions, kernel cancellation methods (Nakagawa, 1993), the auxiliary surface of "tent" method (Lutz et al, 1992), and the line integral method (Krishnasamy et al, 1994, Liu et al, 1993, and Liu, 1998. Sladek et al (2001) proposed a semi-analytical integration scheme to deal with the logarithmic singularity in BEM.…”

Section: Introductionmentioning

confidence: 99%

Regularization of nearly singular integrals in the boundary element analysis for interior anisotropic thermal field near the boundary

Shiah

Shih²

2007

Journal of the Chinese Institute of Engineers

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In this paper the previously developed scheme of integration by parts to treat the boundary thermal field is applied to calculate the interior thermal field. Also, the scheme is extended further to regularize the strongly singular integral appearing in the boundary integral equation for interior calculations of the heat fluxes. Moreover, the present work develops a semi-analytical integration scheme to regularize the hypersingular integral for the interior heat-flux calculations. All formulations are derived for elements of arbitrary orders with general interpolation. At the end, the veracity of the scheme is illustrated by numerical examples.

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“…Considerable effort has been put into this so-called thin-body problem in recent years in order to make it tractable with BEM, and different formulations have been proposed that can alleviate or remove such difficulties. [1][2][3][4] There is a second family of cases that shares many features with thin bodies. This may be named the narrow-gap problem.…”

Section: Introductionmentioning

confidence: 99%

“…4 First, the coefficient matrix becomes ill-conditioned as the distance gets smaller, and second, the integrals are near singular and difficult to solve numerically. The methods proposed to get around these difficulties in the thin-body variant fall into two groups: multidomain methods and normal-derivative equation methods.…”

Section: Introductionmentioning

confidence: 99%

“…assume the approximation of an infinitely thin body, applies the HIE on one side of the thin body and its normal derivative on the other. 4 For a plane narrow gap a multidomain strategy could be used in which the gap could be modeled as a twodimensional problem coupled to an exterior threedimensional problem. However, this approach is only approximate for any finite gap width, and not suitable for problems where the sound field details inside the gap are important.…”

Section: Introductionmentioning

confidence: 99%

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On the modeling of narrow gaps using the standard boundary element method

Cutanda

Juhl²,

Jacobsen

2001

The Journal of the Acoustical Society of America

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Numerical methods based on the Helmholtz integral equation are well suited for solving acoustic scattering and diffraction problems at relatively low frequencies. However, it is well known that the standard method becomes degenerate if the objects that disturb the sound field are very thin. This paper makes use of a standard axisymmetric Helmholtz integral equation formulation and its boundary element method (BEM) implementation to study the behavior of the method on two test cases: a thin rigid disk of variable thickness and two rigid cylinders separated by a gap of variable width. Both problems give rise to the same kind of degeneracy in the method, and modified formulations have been proposed to overcome this difficulty. However, such techniques are better suited for the so-called thin-body problem than for the reciprocal narrow-gap problem, and only the first is usually dealt with in the literature. A simple integration technique that can extend the range of thicknesses/widths tractable by the otherwise unmodified standard formulation is presented and tested. This technique is valid for both cases. The modeling of acoustic transducers like sound intensity probes and condenser microphones has motivated this work, although the proposed technique has a wider range of applications.

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Boundary integral equations for thin bodies

Cited by 88 publications

References 15 publications

Sound pressure attenuation provided by a 3D rigid acoustic barrier on a building façade: the influence of its longitudinal shape

Sound pressure attenuation provided by a 3D rigid acoustic barrier on a building façade: the influence of its longitudinal shape

Regularization of nearly singular integrals in the boundary element analysis for interior anisotropic thermal field near the boundary

On the modeling of narrow gaps using the standard boundary element method

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