Mapped Wave Envelope Elements for Acoustical Radiation and Scattering

Astley, R.J.; Macaulay, Gavin J.; Coyette, Jean‐Pierre

doi:10.1006/jsvi.1994.1048

Cited by 151 publications

(110 citation statements)

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“…Astley et al [14], [15] and Li [16] used infinite wave envelope elements combined with conventional finite elements to model the transient wave equation in unbounded regions. The method was based on a Fourier transform of the wave envelope approach applied to steady wave problems and was valid over a full range of excitation frequencies.…”

Section: Wave Envelopementioning

confidence: 99%

Methods in Solving the Wave Equations for A Loudspeaker

Zeng¹,

Wang²,

Dong³

2012

Proceedings of the 2012 2nd International Conference on Computer and Information Applications (ICCIA 2012)

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Abstract-This paper introduces several methods in solving the wave equations for a loudspeaker. The separation of variables method is very common for solving constant coefficient linear partial differential problems. The finite difference method has been the main method of numerical computation in early work. The direct method is to formulate the boundary integral equation and can be solved using a direct time integration procedure. There are also some transform methods such as Fourier, Laplaces and wavelet transforms etc. to solve the wave equations. The retarded potential technique to solve the wave problems numerically was first used in the early 1960s. Since then, many authors have worked on the method and its applications.

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Section: Wave Envelopementioning

confidence: 99%

Methods in Solving the Wave Equations for A Loudspeaker

Zeng¹,

Wang²,

Dong³

2012

Proceedings of the 2012 2nd International Conference on Computer and Information Applications (ICCIA 2012)

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“…Lower order weighting functions are used in the third formulation to avoid this evaluation, and from Figure 4 it is seen that this gives greater accuracy. We therefore shall only use the third formulation, which uses Astley wave envelope inÿnite elements [7], to model the inÿnite element domain in the rest of the paper.…”

Section: Accuracy Over Inÿnite Elementsmentioning

confidence: 99%

“…We consider Astley's approach [7] using weighting functions of lower order in the ÿeld variable r so that the contour integral contribution tends to zero as r tends to inÿnity. The natural choice would be to obtain the weighting functions by multiplying the shape functions by a factor = √ r where is chosen so that the function has nodal value one.…”

Section: Third Formulationmentioning

confidence: 99%

“…If di erent weighting functions, multiplied by an additional factor r −1 , are considered then a third formulation is obtained in which the contour integral contribution is zero. This gives an Astley-type [7] mapped wave envelope formulation. The three formulations are tested for some simple problems.…”

Section: Introductionmentioning

confidence: 99%

“…The determination of the resulting integral expression proved complicated, and special integration rules were developed. Astley [5][6][7] later introduced a complex conjugate weighting, which simpliÿes the integrand greatly so that it can be evaluated using Gauss-Legendre integration. Chadwick and Bettess [1; 8] give an equivalent approach for bounded ÿnite domain problems by choosing the governing equation for the wave envelope and the phase rather than for the potential.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Diffraction of short waves modelled using new mapped wave envelope finite and infinite elements

Chadwick

Bettess

Laghrouche

1999

Int. J. Numer. Meth. Engng.

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SUMMARYWe consider a two-dimensional wave di raction problem from a closed body such that the complex progressive wave potential satisÿes the Sommerfeld condition and the Helmholtz equation. We are interested in the case where the wavelength is much smaller than any other length dimensions of the problem. We introduce new mapped wave envelope inÿnite elements to model the potential in the far ÿeld, and test them for some simple Dirichlet boundary condition problems. They are used in conjuction with wave envelope ÿnite elements developed earlier [1] to model the potential in the near ÿeld. An iterative procedure is used in which an initial estimate of the phase is iteratively improved. The iteration scheme, by which the wave envelope and phase are recovered, is described in detail.

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Finite element formulations for exterior problems: application to hybrid methods, non-reflecting boundary conditions, and infinite elements

Harari

Barbone

Montgomery

1997

Int. J. Numer. Meth. Engng.

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SUMMARYWe develop formulations for ÿnite element computation of exterior acoustics problems. A prominent feature of the formulations is the lack of integration over the unbounded domain, simplifying the task of discretization and potentially leading to numerous additional beneÿts. These formulations provide a suitable basis for hybrid asymptotic-numerical methods in scattering, non-re ecting boundary conditions and inÿnite elements. ? 1997 by John Wiley & Sons, Ltd.

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Mapped Wave Envelope Elements for Acoustical Radiation and Scattering

Cited by 151 publications

References 0 publications

Methods in Solving the Wave Equations for A Loudspeaker

Methods in Solving the Wave Equations for A Loudspeaker

Diffraction of short waves modelled using new mapped wave envelope finite and infinite elements

Finite element formulations for exterior problems: application to hybrid methods, non-reflecting boundary conditions, and infinite elements

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