On the solution of boundary value problems using spheroidal eigenvectors

Charalambopoulos, A.; Fotiadis, Dimitrios I.; Kourounis, Drosos; Massalas, C.V.

doi:10.1016/s0010-4655(01)00206-5

Cited by 8 publications

(5 citation statements)

References 13 publications

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“…That is why there are no pure TE or TM modes in spheroids but only hybrid ones. Different methods of separation of variables (SVM) using series expansions with either spheroidal or spherical functions have been proposed [11], [12], [13]. Unfortunately they lead to extremely bulky infinite sets of equations which can be solved numerically only in simplest cases and the convergence is not proved.…”

Section: Introductionmentioning

confidence: 99%

Geometrical theory of whispering-gallery modes

Gorodetsky

Fomin

2006

IEEE J. Select. Topics Quantum Electron.

142

120

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Abstract-Using quasiclassical approach rather precise analytical approximations for the eigenfrequencies of whispering gallery modes in convex axisymmetric bodies may be found. We use the eikonal method to analyze the limits of precision of quasiclassical approximation using as a practical example spheroidal dielectric cavity. The series obtained for the calculation of eigenfrequencies is compared with the known series for dielectric sphere and with numerical calculations. We show how geometrical interpretation allows expansion of the method on arbitrary shaped axisymmetric bodies.

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Section: Introductionmentioning

confidence: 99%

Geometrical theory of whispering-gallery modes

Gorodetsky

Fomin

2006

IEEE J. Select. Topics Quantum Electron.

142

120

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“…Thus, it can model much better than the spherical geometry, a large variety of inclusions or inhomogeneities participating in scattering processes. [1][2][3][4][5] A lot of effort has been devoted to study the direct scattering problem by obstacles [6][7][8][9][10][11][12][13] and especially from spheroids both theoretically and numerically. The adopted methodology in each case depends crucially on the frequency (wavenumber) range under consideration.…”

Section: Introductionmentioning

confidence: 99%

Numerical investigation of the acoustic scattering problem from penetrable prolate spheroidal structures using the Vekua transformation and arbitrary precision arithmetic

Gergidis

Kourounis

Mavratzas³

et al. 2018

Math Methods in App Sciences

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A complete set of radiating “outwards” eigensolutions of the Helmholtz equation, obtained by transforming appropriately through the Vekua mapping the kernel of Laplace equation, is applied to the investigation of the acoustic scattering by penetrable prolate spheroidal scatterers. The scattered field is expanded in terms of the aforementioned set, detouring so the standard spheroidal wave functions along with their inherent numerical deficiencies. The coefficients of the expansion are provided by the solution of linear systems, the conditioning of which calls for arbitrary precision arithmetic. Its integration enables the polyparametric investigation of the convergence of the current approach to the solution of the direct scattering problem. Finally, far‐field pattern visualization in the 3D space clarifies the preferred scattering directions for several frequencies of the incident wave, ranging from the “low” to the “resonance” region.

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“…Different methods of separation of variables (SVM) using series expansions with either spheroidal or spherical functions have been proposed. [11][12][13] Unfortunately they lead to extremely bulky infinite sets of equations which can be solved numerically only in simplest cases and the convergence is not proved. Exact characteristic equation for the eigenfrequencies in dielectric spheroid was suggested 14 without provement that if real could significantly ease the task of finding eigenfrequencies.…”

Section: Introductionmentioning

confidence: 99%

<title>Whispering gallery modes in axisymmetric resonators</title>

Gorodetsky

Fomin

2008

SPIE Proceedings

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Using quasiclassical approach rather precise analytical approximations for the eigenfrequencies of whispering gallery modes in convex axisymmetric bodies may be found. We use the eikonal method to analyze the limits of precision of this approach using as a practical example spheroidal dielectric cavity. The series obtained for the calculation of eigenfrequency is compared with the known series for dielectric sphere and numerical calculations.

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On the solution of boundary value problems using spheroidal eigenvectors

Cited by 8 publications

References 13 publications

Geometrical theory of whispering-gallery modes

Geometrical theory of whispering-gallery modes

Numerical investigation of the acoustic scattering problem from penetrable prolate spheroidal structures using the Vekua transformation and arbitrary precision arithmetic

<title>Whispering gallery modes in axisymmetric resonators</title>

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