Frequency-Domain Edge Diffraction for Finite and Infinite Edges

2013

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The secondary edge source line integral formulation for diffraction modeling uses edge sources with a 1/r dependency, in addition to a directivity function. At first sight, this might seem to contradict the expected 1/r behavior for the gradient near the edge of a thin screen. An analysis is presented for the special case of perpendicular plane wave incidence onto a thin screen, which shows that the secondary edge source formulation does indeed lead to the expected behavior close to the edge of an ideal wedge.

Section: The Secondary Edge Source Line Integralmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

The diffracted field and its gradient near the edge of a thin screen

Hewett

2013

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“…The diffraction components for the scattering by an infinite wedge are well known [2,16]. The diffraction wave can in this case be written as a line integral along the edge, with an integrand which includes spherical divergence factors as well as analytical directivity factors, and with the position along the physical wedge as integration variable, either in the time-domain [24] or frequency domain [23]. A Figure 2: A single wedge.…”

Section: Diffraction From a Finite Wedgementioning

confidence: 99%

An integral equation formulation for the diffraction from convex plates and polyhedra

Asheim

2013

A new formulation of the problem of scattering from obstacles with edges is presented. The formulation is based on decomposing the field into geometrical optics and edge diffraction components, as opposed to the usual incident and scattered wavefields used for BEM and FEM methods. A secondary-source model is available for edgediffraction, which is extended to handle multiple diffraction of all orders. We show that the diffraction component can be represented by the solution of an integral equation formulated on pairs of edge points, so that the total field can be evaluated as as sum of geometrical optics and this diffraction component. Numerical experiments demonstrates the validity of the approach for wavenumbers down to 0.Keywords : Scattering, diffraction, integral equations, convex plates, convex polyhedra MSC : Primary : 65R20, Secondary : 45B05, 78A05, 78A45. An integral equation formulation for the diffraction from convex plates and polyhedraAndreas Asheim * U. Peter Svensson † March 5, 2012Abstract A new formulation of the problem of scattering from obstacles with edges is presented. The formulation is based on decomposing the field into geometrical optics and edge diffraction components, as opposed to the usual incident and scattered wavefields used for BEM and FEM methods. A secondary-source model is available for edge-diffraction, which is extended to handle multiple diffraction of all orders. We show that the diffraction component can be represented by the solution of an integral equation formulated on pairs of edge points, so that the total field can be evaluated as as sum of geometrical optics and this diffraction component. Numerical experiments demonstrates the validity of the approach for wavenumbers down to 0.

“…This work explores the exact frequency-domain solution for the first-order diffraction wave from finite edges as proposed by Svensson, Calamia and Nakanishi, 8 which is a reformulation of the solution for infinite edges by Bowman and Senior, 2 and Pierce. 3 The solution takes the form of a line integral with an oscillatory integrand, a Fourier-type integral to be precise, which is increasingly oscillatory for increasing frequencies.…”

Section: And Othersmentioning

confidence: 99%

“…In that case the integration would be done over the interval ͓ −5,5͔ \ ͓z a − z split , z a + z split ͔ where z split is chosen as described by Svensson et al,8 such that it scales linearly with 1 / ͱ k.…”

Section: B Breakdown Near Zone Boundariesmentioning

confidence: 99%

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

Asheim

2010

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For the problem of edge diffraction from an edge of finite length a frequency-domain solution, obtained from an analytical time-domain solution, has been presented by Svensson et al. [Acta. Acust. Acust. 95, 568-572]. This formulation takes the form of a Fourier-type integral whose evaluation is expensive in the high frequency range. This paper demonstrates that by using tailored highly oscillatory quadrature methods based on asymptotic properties of the integral, accurate approximations in the high frequency case can be obtained with little computational effort.