Equations intégrales volumiques pour la diffraction d'ondes électromagnétiques par un corps diélectrique

Abstract : We are concerned with studying the electromagnetic scattering by a dielectric body. From Maxwell equations, we derived two integral formulations. One is a volume integral equation with a strongly singular kernel and the other one is a coupled surface-volume integral equation with a weakly singular kernel. Assuming a discontinuous electric permittivity across the dielectric boundary, the two formulations are analyzed using standard Fredholm properties. The hypothesis of discontinuity for the electric permittivity is more realistic and moreover it enables composite dielectric materials with several surfaces of discontinuity. The volume integral equation is then solved numerically. To this end, we developed a method to handle the singularities in the kernel of the volume integral operator. This method of treatment of singularities is based on changes of variables involving Duffy transformations and it can be applied to a wide class of integral operator. The method and the volume integral equation are implemented in the Mélina++ code which is a finite element library developed within the mathematical research institut of Rennes. We complete the work with some numerical tests results.
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https://tel.archives-ouvertes.fr/tel-00504939
Contributor : El Hadji Koné <>
Submitted on : Thursday, July 22, 2010 - 5:13:27 AM
Last modification on : Thursday, November 15, 2018 - 11:56:21 AM
Long-term archiving on : Tuesday, October 23, 2012 - 10:50:20 AM

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  • HAL Id : tel-00504939, version 1

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El Hadji Koné. Equations intégrales volumiques pour la diffraction d'ondes électromagnétiques par un corps diélectrique. Mathématiques [math]. Université Rennes 1, 2010. Français. ⟨tel-00504939⟩

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