Asymptotic expansion of the solution of Maxwell’s equations in polygonal plane domains

نویسنده

  • Boniface Nkemzi
چکیده

This paper is mainly concerned with the structure of the singular and regular parts of the solution of time-harmonic Maxwell's equations in polygonal plane domains. The asymptotic behaviour of the solution near corner points of the domain is studied by means of discrete Fourier transformation. A detailed functional analysis of the solution shows that the boundary value problem does not belong locally to H 2 when the boundary of the domain has non-acute angles, and explicit formulas for the singularity functions and their corresponding coefficients are given. Développement asymptotique de la solution des équations de Maxwell dans des domaines polygonaux Résumé : Cet article étudie la structure des singularités de la solution des équations de Maxwell harmoniques dans des polygones plans. Le comportement asymptotique de la solution au voisinage des coins est étudié à l'aide de séries de Fourier. Une analyse détaillée du problème aux limites montre que la solution n'est pas localement H 2 lorsque la frontière du domaine présente des angles obtus ou rentrants, On présente des formules explicites pour les fonctions singulières et les coefficients de singularité. Mots-clés : Équations de Maxwell, singularités, méthode de Fourier.

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تاریخ انتشار 2005