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Theoretical tools to solve the axisymmetric Maxwell equations

Franck Assous 1, 2 Patrick Ciarlet 3 Simon Labrunie 2 
3 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : In this paper, the mathematical tools, which are required to solve the axisymmetric Maxwell equations, are presented. An in-depth study of the problems posed in the meridian half-plane, numerical algorithms, as well as numerical experiments, based on the implementation of the theory described hereafter, shall be presented in forthcoming papers. In the present paper, the attention is focused on the (orthogonal) splitting of the electromagnetic field in a regular part and a singular part, the former being in the Sobolev space H-1 component-wise. It is proven that the singular fields are related to singularities of Laplace-like operators, and, as a consequence, that the space of singular fields is finite dimensional. Copyright (C) 2002 John Wiley Sons, Ltd.
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Submitted on : Monday, November 4, 2013 - 1:47:30 PM
Last modification on : Wednesday, May 11, 2022 - 12:06:04 PM

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Franck Assous, Patrick Ciarlet, Simon Labrunie. Theoretical tools to solve the axisymmetric Maxwell equations. Mathematical Methods in the Applied Sciences, 2002, 25 (1), pp.49-78. ⟨10.1002/mma.279⟩. ⟨hal-00878222⟩



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