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

Hewett, David P.; Svensson, U. Peter

doi:10.1121/1.4828824

Cited by 3 publications

(4 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The formula for β D above corrects that in Ref. 11 by reversing the sign of β D . Also, the first expression for η in Eq.…”

Section: Edge Source Integral For Ideal Wedgessupporting

confidence: 69%

See 1 more Smart Citation

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

Hewett

2015

The Journal of the Acoustical Society of America

Self Cite

View full text Add to dashboard Cite

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 However, when surface waves are present the physical interpretation of the edge source integral must be altered: it no longer represents solely the diffracted field, but rather it includes surface wave contributions.

show abstract

“…The formula for β D above corrects that in Ref. 11 by reversing the sign of β D . Also, the first expression for η in Eq.…”

Section: Edge Source Integral For Ideal Wedgessupporting

confidence: 69%

“…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

Self Cite

View full text Add to dashboard Cite

show abstract

“…This arrangement is consistent with the expectation that Ũtotal ! 0 at the edge of the panel 59 and meets the continuity requirements of H. 60 Pressure at receiver locations can be evaluated by U scat ðxÞ ¼ Df Ũtotal gðxÞ þikYSf U total gðxÞ. Following the same logic used to derive this statement, 61 it can be asserted that the equivalent statement for spherical harmonic coefficients will also hold: A scat m;n ¼ ikD in m;n f Ũtotal gðxÞ À k 2 YS in m;n f U total gðxÞ.…”

Section: Scenementioning

confidence: 99%

A framework for auralization of boundary element method simulations including source and receiver directivity

Hargreaves

Rendell

Lam

2019

The Journal of the Acoustical Society of America

View full text Add to dashboard Cite

The Boundary Element Method (BEM) is a proven numerical prediction tool for computation of room acoustic transfer functions, as are required for auralization of a virtual space. In this paper, it is validated against case studies drawn from the "Ground Truth for Room Acoustical Simulation" database within a framework that includes source and receiver directivity. These aspects are often neglected but are respectively important to include for auralisation applications because source directivity is known to affect how a room is excited and because the human auditory system is sensitive to directional cues. The framework uses weighted-sums of spherical harmonic functions to represent both the source directivity to be simulated and the pressure field predicted in the vicinity of the receiver location, the coefficients of the former being fitted to measured directivity and those of the latter computed directly from the boundary data by evaluating a boundary integral. Three validation cases are presented, one of which includes a binaural receiver. The computed results match measurements closely for the two cases conducted in anechoic conditions but show some significant differences for the third room scenario; here, it is likely that uncertainty in boundary material data limited modelling accuracy.

show abstract

“…Equivalent behaviour is seen in line-integral representations of scattering from sound hard wedges (e.g. Equation (4) of [27]). …”

Section: Computing the Gradient Of ‰ Jmentioning

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

View full text Add to dashboard Cite

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.

show abstract

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

Cited by 3 publications

References 9 publications

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

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

A framework for auralization of boundary element method simulations including source and receiver directivity

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

Contact Info

Product

Resources

About