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Theoretical tools to solve the axisymmetric Maxwell equations

✍ Scribed by F. Assous; P. Ciarlet Jr.; S. Labrunie

Publisher
John Wiley and Sons
Year
2001
Tongue
English
Weight
235 KB
Volume
25
Category
Article
ISSN
0170-4214

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✦ Synopsis

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. This paper can be viewed as the continuation of References (J. Comput. Phys. 2000; 161: 218–249, ModΓ©l. Math. Anal. NumΓ©r, 1998; 32: 359–389) Copyright Β© 2002 John Wiley & Sons, Ltd.

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