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Theoretical tools to solve the axisymmetric Maxwell equations
Author(s) -
Assous F.,
Ciarlet P.,
Labrunie S.
Publication year - 2001
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.279
Subject(s) - gravitational singularity , mathematics , maxwell's equations , laplace transform , rotational symmetry , sobolev space , mathematical analysis , space (punctuation) , numerical analysis , calculus (dental) , computer science , geometry , medicine , dentistry , operating system
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, Modél. Math. Anal. Numér , 1998; 32 : 359–389) Copyright © 2002 John Wiley & Sons, Ltd.