Efficient evaluation of edge diffraction integrals using the numerical method of steepest descent

Asheim, Andreas; Svensson, U. Peter

doi:10.1121/1.3479545

Cited by 10 publications

(3 citation statements)

References 19 publications

(23 reference statements)

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“…An efficient method for computing the resulting integrals waslater presented by Asheim and Svensson [30]. The higher-order diffraction term, G hod ,can be computed for convex,r igid scattering objects via an integral equation, as shown in [28].…”

Section: Edge Diffractionmentioning

confidence: 99%

Using Mode Matching Methods and Edge Diffraction in Horn Loudspeaker Simulation

Kolbrek¹,

Svensson²

2015

Acta Acustica united with Acustica

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Amethod for simulating an expanding duct, likeahorn, by mode matching techniques is described. Forahorn in an infinite baffle, the modal radiation impedance and radiated pressure can be found from known relations. For ahorn equipped with asmall baffleorflange, however, diffraction from the edges has to be taken into account. This paper investigates howa ne dge diffraction term can be included, and its effect on the throat and radiation impedances and radiated pressure. Measurement results are presented, and are shown to be in good agreement with the simulations, both for ahorn in alarge baffle, and for ahorn with asmall flange.

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Section: Edge Diffractionmentioning

confidence: 99%

Using Mode Matching Methods and Edge Diffraction in Horn Loudspeaker Simulation

Kolbrek¹,

Svensson²

2015

Acta Acustica united with Acustica

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“…Electronic mail: hewett@maths.ox.ac.uk ficient numerical evaluation of the line integrals has been considered in Ref. 9 using the method of numerical steepest descent, as has the behaviour of the line integrals near shadow boundaries 10 and edges 11 . Note also Ref.…”

Section: Introductionmentioning

confidence: 99%

Diffraction by a right-angled impedance wedge: An edge source formulation

Hewett

2015

The Journal of the Acoustical Society of America

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This paper concerns the frequency domain problem of diffraction of a plane wave incident on an infinite right-angled wedge on which impedance (absorbing) boundary conditions are imposed. It is demonstrated that the exact Sommerfeld-Malyuzhinets contour integral solution for the diffracted field can be transformed to a line integral over a physical variable along the diffracting edge. This integral can be interpreted as a superposition of secondary point sources (with directivity) positioned along the edge, in the spirit of the edge source formulations for rigid (sound-hard) wedges derived by Svensson et al. [Acta Acust. Acust. 95, 568-572 (2009)]. However, when surface waves are present the physical interpretation of the edge source integral must be altered: it no longer represents solely the diffracted field, but rather it includes surface wave contributions.

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“…This should be relatively straightforward for the polygonal elements considered herein, because the contour integral kernels are extremely similar to those that occur in the Biot-Tolstoy-Medwin expression for diffraction from an infinite rigid wedge, and the method of steepest descent has already been applied to this [29]. This would reduce the computational complexity to be k-independent, which would make this integration approach extremely competitive for HF-BEM methods operating with extremely large k.…”

Section: Conclusion and Further Workmentioning

confidence: 99%

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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Efficient evaluation of edge diffraction integrals using the numerical method of steepest descent

Cited by 10 publications

References 19 publications

Using Mode Matching Methods and Edge Diffraction in Horn Loudspeaker Simulation

Using Mode Matching Methods and Edge Diffraction in Horn Loudspeaker Simulation

Diffraction by a right-angled impedance wedge: An edge source formulation

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

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