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Journal articles
Weighted regularization for composite materials in electromagnetism
Abstract : In this paper, a weighted regularization method for the time-harmonic Maxwell equations with perfect conducting or impedance boundary condition in composite materials is presented. The computational domain Ω is the union of polygonal or polyhedral subdomains made of different materials. As a result, the electromagnetic field presents singularities near geometric singularities, which are the interior and exterior edges and corners. The variational formulation of the weighted regularized problem is given on the subspace of H(curl;Ω) whose fields u satisfy wα div(εu) ∈ L 2(Ω) and have vanishing tangential trace or tangential trace in L2(δΩ). The weight function w(x) is equivalent to the distance of x to the geometric singularities and the minimal weight parameter α is given in terms of the singular exponents of a scalar transmission problem. A density result is proven that guarantees the approximability of the solution field by piecewise regular fields. Numerical results for the discretization of the source problem by means of Lagrange Finite Elements of type P1 and P2 are given on uniform and appropriately refined two-dimensional meshes. The performance of the method in the case of eigenvalue problems is addressed. © EDP Sciences, SMAI 2009.
Mots-clés :
Modèle mathématique
Analyse numérique
Problème valeur propre
Calcul 2 dimensions
Méthode élément fini
Méthode discrétisation
Solution régulière
Problème transmission
Fonction poids
Champ électromagnétique
Condition aux limites
Équation Maxwell
Électromagnétisme
Matériau composite
Méthode régularisation
Régularisation
Problème mal posé
Algèbre linéaire numérique
https://hal-ensta-paris.archives-ouvertes.fr//hal-00873065
Contributor : Aurélien Arnoux <>
Submitted on : Wednesday, October 16, 2013 - 2:04:25 PM
Last modification on : Tuesday, May 26, 2020 - 8:12:03 AM
Contributor : Aurélien Arnoux <>
Submitted on : Wednesday, October 16, 2013 - 2:04:25 PM
Last modification on : Tuesday, May 26, 2020 - 8:12:03 AM
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