A characterization of singular electromagnetic fields by an inductive approach

F. Assous 1 Patrick Ciarlet 2 E. Garcia 3
2 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 article, we are interested in the mathematical modeling of singular electromagnetic fields, in a non-convex polyhedral domain. We first describe the local trace (i. e. defined on a face) of the normal derivative of an L2 function, with L2 Laplacian. Among other things, this allows us to describe dual singularities of the Laplace problem with homogeneous Neumann boundary condition. We then provide generalized integration by parts formulae for the Laplace, divergence and curl operators. With the help of these results, one can split electromagnetic fields into regular and singular parts, which are then characterized. We also study the particular case of divergence-free and curl-free fields, and provide non-orthogonal decompositions that are numerically computable. © 2008 Institute for Scientific Computing and Information.
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Submitted on : Thursday, October 17, 2013 - 2:18:43 PM
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F. Assous, Patrick Ciarlet, E. Garcia. A characterization of singular electromagnetic fields by an inductive approach. International Journal of Numerical Analysis and Modeling, Institute for Scientific Computing and Information, 2008, 5 (3), pp.491-515. ⟨hal-00873083⟩



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