Theoretical tools to solve the axisymmetric Maxwell equations

F. Assous, P. Ciarlet, S. Labrunie

Research output: Contribution to journalArticlepeer-review

40 Scopus citations


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 H1 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).

Original languageEnglish
Pages (from-to)49-78
Number of pages30
JournalMathematical Methods in the Applied Sciences
Issue number1
StatePublished - 10 Jan 2002
Externally publishedYes


  • Axisymmetry
  • Conical vertices
  • Maxwell equations
  • Reentrant edges
  • Singularities


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