Line integrals and physical optics Part II The conversion of the Kirchhoff surface integral to a line integral

Asvestas, John S.

doi:10.1364/josaa.2.000896

Cited by 43 publications

(15 citation statements)

References 6 publications

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“…The terms used to discretise the surface quantities are therefore defined not only on the surface but also as waves in the medium. If these basis functions satisfy the wave equation then it can be shown (using a transform developed for the problem of aperture diffraction [12,13,14]) that their scattering can be stated as a geometric term plus an edge-diffraction contour integral. Since the contour integrals are 1D it follows that they can be evaluated in ( ) operations, so scale better than standard quadrature methods.…”

Section: 'Wave-matching' Methodsmentioning

confidence: 99%

Toward a full-bandwidth numerical acoustic model

Hargreaves

Lam

2013

The Journal of the Acoustical Society of America

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Prediction models are at the heart of modern acoustic engineering and are used in a diverse range of applications from refining the acoustic design of classrooms and concert halls to predicting how noise exposure varies through an urban environment. They also allow Auralisation to be performed for buildings and spaces before they are built or long after they are lost. Current commercial room acoustic simulation software almost exclusively approximates the propagation of sound geometrically as rays or beams. These assumptions yield efficient algorithms, but the maximum accuracy they can achieve is limited by how well the geometric assumption represents sound propagation in a given space. This compromises their accuracy at low frequencies in particular. Methods that directly model wave effects are more accurate but they have a computational cost that scales with problem size and frequency, effectively limiting them to small or low frequency scenarios. This paper will report the results of ongoing research into a new algorithm which aims to be accurate and efficient for all frequencies; the name proposed for this is the "Wave Matching Method". This builds on the Boundary Element Method with the premise that if an appropriate interpolation scheme is designed then the model will become 'geometric ally dominated' at high frequencies. Other propagation modes may then be removed without significant error, yielding an algorithm which is accurate and efficient. This paper will present the general concepts of the algorithm and progress to date.

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Section: 'Wave-matching' Methodsmentioning

confidence: 99%

Toward a full-bandwidth numerical acoustic model

Hargreaves

Lam

2013

The Journal of the Acoustical Society of America

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“…First it bears a very close resemblance to the energy-inspired time domain BEM algorithms in references 13 and 14, for which unconditional stability can be proven. Secondly it bears a close resemblance to the scattering integral, suggesting that transformation to an edge integral for efficient evaluation may be possible; this has yet to be shown but Asvestas 15 gives a process for converting double integrals of this form into contour integrals. Substituting ‫)ܠ(߮‬ = ‫)ܠ(߰‬ + ‫)ܠ(߯‬ and then breaking down ‫)ܠ(߰‬ into a sum of waves ߰ ܽ,݉ ,݊ f ‫)ܠ(‬ scattered by each basis function yields:…”

Section: Figure 2 Conceptual Separation Of Medium and Obstacle Modelsmentioning

confidence: 99%

Towards a full-bandwidth numerical acoustic model

Hargreaves¹,

Lam²

2013

Proceedings of Meetings on Acoustics

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Prediction models are at the heart of modern acoustic engineering. Current commercial room acoustic simulation software almost exclusively approximates the propagation of sound geometrically as rays or beams. These assumptions yield efficient algorithms, but the maximum accuracy they can achieve is limited by how well the geometric assumption represents sound propagation in a given space. This comprises their accuracy at low frequencies in particular. Methods that directly model wave effects are more accurate but they have a computational cost that scales with problem size and frequency, effectively limiting them to small or low frequency scenarios. This paper will report the results of initial research into a new full-bandwidth model which aims to be accurate and efficient for all frequencies; the name proposed for this is the "Wave Matching Method". This builds on the Boundary Element Method with the premise that if an appropriate interpolation scheme is designed then the model will become 'geometrically dominated' at high frequencies. Other propagation modes may then be removed without significant error, yielding an algorithm which is accurate and efficient. This paper will present the general concepts of wave matching and the results from some numerical test cases.

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“…However, such an indubitable computational advantage is balanced by the presence of singularities in the integrand of the one-dimensional BDW integral, which gives numerical problems, especially whenever the BDW field has to be evaluated close to the geometrical shadow at the observation plane [8]. To overcome such difficulties, important modifications to the BDW theory were provided by several authors [9][10][11][12][13][14][15]. In 2000, Hannay [16] showed that, when the BDW integral (for spherical or plane wave illumination) is written within paraxial approximation, it takes on a mathematical form in which the above singularities are no longer present.…”

Section: Introductionmentioning

confidence: 99%

Uniform asymptotics of paraxial boundary diffraction waves

Borghi

2015

J. Opt. Soc. Am. A

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Starting from the paraxial formulation of the boundary-diffracted-wave theory proposed by Hannay [J. Mod. Opt. 47, 121-124 (2000)] and exploiting its intrinsic geometrical character, we rediscover some classical results of Fresnel diffraction theory, valid for "large" hard-edge apertures, within a somewhat unorthodox perspective. In this way, a geometrical interpretation of the Schwarzchild uniform asymptotics of the paraxially diffracted wavefield by circular apertures [K. Schwarzschild, Sitzb. München Akad. Wiss. Math.-Phys. Kl. 28, 271-294 (1898)] is given and later generalized to deal with arbitrarily shaped apertures with smooth boundaries. A quantitative exploration is then carried out, with the language of catastrophe optics, about the diffraction patterns produced within the geometrical shadow by opaque elliptic disks under plane wave illumination. In particular, the role of the ellipse's evolute as a geometrical caustic of the diffraction pattern is emphasized through an intuitive interpretation of the underlying saddle coalescing mechanism, obtained by suitably visualizing the saddle topology changes induced by letting the observation point move along the ellipse's major axis.

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Line integrals and physical optics Part II The conversion of the Kirchhoff surface integral to a line integral

Cited by 43 publications

References 6 publications

Toward a full-bandwidth numerical acoustic model

Toward a full-bandwidth numerical acoustic model

Towards a full-bandwidth numerical acoustic model

Uniform asymptotics of paraxial boundary diffraction waves

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