Acoustic scattering by a sphere in the time domain

Martin, P. A.

doi:10.1016/j.wavemoti.2016.07.007

Cited by 10 publications

(6 citation statements)

References 27 publications

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“…The time dependent coefficients of such expansions turn out to grow exponentially with increasing order. As a consequence, a loss of significant figures will result from cancellations between terms of growing magnitude at large times unless new formulations are used to calculate the coefficients [Greengard et al 2014, Martin 2016a, Martin 2016b.…”

Section: Stability Of Series Solutionsmentioning

confidence: 99%

“…Another approach to solving the wave equation is to extend the conventional boundary integral method to the time domain using the time-dependent Green's function to represent the spatial solution in terms of values of the wave function on the boundaries of scatterers and the time evolution is treated by time marching [Groenenboom 1983]. Recently there is renewed theoretical interest in the stability of the time dependent solutions of the wave equation at large times particularly for the canonical problem of scattering by a sphere in an infinite spatial domain for which space and time variations can be represented analytically in terms of infinite series of spherical harmonics and Bessel functions with time-dependent coefficients [Greengard et al 2014, Martin 2016a, Martin 2016b].…”

Section: Introductionmentioning

confidence: 99%

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Space-time domain solutions of the wave equation by a non-singular boundary integral method and Fourier transform

Klaseboer

Sepehrirahnama

Chan

2017

The Journal of the Acoustical Society of America

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The general space-time evolution of the scattering of an incident acoustic plane wave pulse by an arbitrary configuration of targets is treated by employing a recently developed non-singular boundary integral method to solve the Helmholtz equation in the frequency domain from which the fast Fourier transform is used to obtain the full space-time solution of the wave equation. The non-singular boundary integral solution can enforce the radiation boundary condition at infinity exactly and can account for multiple scattering effects at all spacings between scatterers without adverse effects on the numerical precision. More generally, the absence of singular kernels in the non-singular integral equation confers high numerical stability and precision for smaller numbers of degrees of freedom. The use of fast Fourier transform to obtain the time dependence is not constrained to discrete time steps and is particularly efficient for studying the response to different incident pulses by the same configuration of scatterers. The precision that can be attained using a smaller number of Fourier components is also quantified.

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Section: Stability Of Series Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Space-time domain solutions of the wave equation by a non-singular boundary integral method and Fourier transform

Klaseboer

Sepehrirahnama

Chan

2017

The Journal of the Acoustical Society of America

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“…Time-domain representations of spherical harmonics expansion have drawn attention in electromagnetics research, motivated by the development of ultra-wideband systems operating with short pulse signals [9][10][11]. Analytical timedomain solutions are studied extensively for scattering problems [11][12][13][14][15][16]. The importance of temporal characteristics is also acknowledged in audio applications, where a bandwidth of about ten octaves is under consideration and the temporal structure is known to have significant impact on human perception of timbre and spaciousness [17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

“…This framework is quite versatile considering that most of the signals are available in digital form. Although not considered in this paper, wave fields can be also modeled with the source signal included [16]. This could be preferred if an analytical representation of the signal is known, e.g.…”

Section: Introductionmentioning

confidence: 99%

Time Domain Sampling of the Radial Functions in Spherical Harmonics Expansions

Hahn

Schultz

Spors

2021

IEEE Trans. Signal Process.

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Spherical harmonics representations are widely adopted in applications such as analysis, manipulation, and synthesis of wave fields that are either captured or simulated. Recent studies have shown that, for broadband fields, a time domain representation of spherical harmonics expansions can benefit from computational efficiency and favorable transient properties. For practical usage, an accurate discrete-time modeling of spherical harmonics expansions is indispensable. The main challenge is to model the so called radial functions which describe the radial and frequency dependencies. In homogeneous cases, they are commonly realized as finite impulse response filters where the coefficients are obtained by sampling the continuoustime representations. This article investigates the temporal and spectral properties of the resulting discrete-time radial functions. The spectral distortions caused by aliasing are evaluated both analytically and numerically, revealing the influence of the distance from the expansion center, sampling frequency, and fractional sample delay. It is also demonstrated how the aliasing can be reduced by employing a recently introduced band limitation method.Index Terms-Radial filter, radial function, time-domain spherical harmonics expansion, time dependent wave field

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“…The method outlined above was first worked out by Jacques Brillouin in 1950 for scattering by a sphere ; see for details and references. Separation of variables in spherical polar coordinates shows that the radial ( r ) part of the solution is given in terms of modified spherical Bessel functions,

k_{n} false(s r / c false), where k_{n} false(z false) = \sqrt{π / (2 z)} K_{n + 1 / 2} false(z false),

and

K_{ν} false(z false)

is a modified Bessel function [, 10.47.9].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Approximations for Radial Spheroidal Wavefunctions with Complex Size Parameter

Martin

2017

Stud Appl Math

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Radial spheroidal wavefunctions are functions of four variables, usually denoted by m, n, x, and γ , the last of which is known as the size parameter. This parameter becomes complex when the problem of scattering of a sound pulse by a spheroid is treated using a Laplace transform with respect to time together with the method of separation of variables. Several asymptotic approximations, involving modified Bessel functions, are developed and analyzed.

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Acoustic scattering by a sphere in the time domain

Cited by 10 publications

References 27 publications

Space-time domain solutions of the wave equation by a non-singular boundary integral method and Fourier transform

Space-time domain solutions of the wave equation by a non-singular boundary integral method and Fourier transform

Time Domain Sampling of the Radial Functions in Spherical Harmonics Expansions

Asymptotic Approximations for Radial Spheroidal Wavefunctions with Complex Size Parameter

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