Modèles et asymptotiques des interfaces fines et périodiques en électromagnétisme

Bérangère Delourme 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, ENSTA ParisTech UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : This work is dedicated to the study of asymptotic models associated with electromagnetic waves scattering from a complex periodic ring. This structure is made of a dielectric ring which contains two layers of wires winding around it. We are interested in situations where both the thickness of the ring and the distance between two consecutive wires are very small compared to the wavelength of the incident wave and the diameter of the ring. One easily understands that in these cases, numerical computation of the solution would become prohibitive as the small scale parameter (denoted by d) goes to 0, since the mesh used needs to accurately follow the geometry of the heterogeneities. In order to overcome this difficulty, we shall derive approximate models where the periodic ring is replaced by effective transmission conditions on the interface S. The numerical discretization of approximate problems is expected to be much less expensive than the exact one, since the mesh no longer needs to be constrained by the small scale. From a technical point of view, these approximate models are derived from the asymptotic expansion of the solution with respect to the small parameter d. Our method mixes matched asymptotic expansions and homogenization. We build the approximate transmission conditions from the truncated expansion. We pay particular attention to the stabilization of the effective transmission conditions. Error estimates and numerical simulations are carried out to validate the accuracy of the models.
Document type :
Analyse numérique [math.NA]. Université Pierre et Marie Curie - Paris VI, 2010. Français
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Submitted on : Saturday, December 10, 2011 - 1:58:04 AM
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Bérangère Delourme. Modèles et asymptotiques des interfaces fines et périodiques en électromagnétisme. Analyse numérique [math.NA]. Université Pierre et Marie Curie - Paris VI, 2010. Français. <tel-00650354>



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