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On singularities of solution of Maxwell's equations in axisymmetric domains with conical points

✍ Scribed by Boniface Nkemzi

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
204 KB
Volume
30
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

Boundary value problems (BVP) in three‐dimensional axisymmetric domains can be treated more efficiently by partial Fourier analysis. Partial Fourier analysis is applied to time‐harmonic Maxwell's equations in three‐dimensional axisymmetric domains with conical points on the rotation axis thereby reducing the three dimensional BVP to an infinite sequence of 2D BVPs on the plane meridian domain Ω~a~⊂ℝ of . The regularity of the solutions u~n~ (n∈ℕ~0~:={0, 1, 2,…}) of the two dimensional BVPs is investigated and it is proved that the asymptotic behaviour of the solutions u~n~ near an angular point on the rotation axis can be characterized by singularity functions related to the solutions of some associated Legendre equations. By means of numerical experiments, it is shown that the solutions u~n~ for n∈ℕ~0~{1} belong to the Sobolev space H^2^ irrespective of the size of the solid angle at the conical point. However, the regularity of the coefficient u~1~ depends on the size of the solid angle at the conical point. The singular solutions of the three dimensional BVP are obtained by Fourier synthesis. Copyright © 2006 John Wiley & Sons, Ltd.

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