Numerical solution to the time-dependent Maxwell equations in axisymmetric singular domains: The Singular Complement Method

Franck Assous Patrick Ciarlet 1 Simon Labrunie Jacques Segré
1 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, we present a method to solve numerically the axisymmetric time-dependent Maxwell equations in a singular domain. In [Math. Methods Appl. Sci. 25 (2002) 49; Math. Methods Appl. Sci. 26 (2003) 861], the mathematical tools and an in-depth study of the problems posed in the meridian half-plane were exposed. The numerical method and experiments based on this theory are now described here. It is also the generalization to axisymmetric problems of the Singular Complement Method that we developed to solve Maxwell equations in 2D singular domains (see [C. R. Acad. Sci. Paris, t. 330 (2000) 391]). It is based on a splitting of the space of solutions in a regular subspace, and a singular one, derived from the singular solutions of the Laplace problem. Numerical examples are finally given, to illustrate our purpose. In particular, they show how the Singular Complement Method captures the singular part of the solution.
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https://hal-ensta-paris.archives-ouvertes.fr//hal-00989621
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Submitted on : Monday, May 12, 2014 - 10:56:44 AM
Last modification on : Thursday, July 4, 2019 - 4:00:50 AM

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Franck Assous, Patrick Ciarlet, Simon Labrunie, Jacques Segré. Numerical solution to the time-dependent Maxwell equations in axisymmetric singular domains: The Singular Complement Method. Journal of Computational Physics, Elsevier, 2003, 191 (1), pp.147-176. ⟨10.1016/S0021-9991(03)00309-7⟩. ⟨hal-00989621⟩

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