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Theses

Analyse Numérique et discrétisation par éléments spectraux avec joints des équations tridimensionnelles de l'électromagnétisme

Abstract : The aim of this thesis is the numerical analysis and the discretisation of Maxwell's equations. The first purpose is to investigate time-harmonic Maxwell's equations in Lipschitz and multiply connected 3D bounded cavities. We prove the wellposedness of the current source problem by means of new formulation. The starting point is the curl-curl second order equation satisfied by the magnetic field. The use of an appropriate compact operator is the heart of the proof. Next, we propose a discretisation relying on spectral element and numerical integration. We prove the convergence of the discrete solution to the exact one and we derive errors estimates. Examples of the numerical solution are given and compared with those obtained by a finite element method in the case of a simple geometry. The last part is to propose a mortar spectral element method for solving heteregeneous Maxwell's equation in 3D bounded cavities. This part is mainly divided into two parts. The method is based on non-conforming decomposition of the domain into the union of non-overlapping parallelipeds. The first part is devoted to the presentation and the numerical analysis of the method. In the second part, we expose some numerical results which confirm the performance of the method.
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https://tel.archives-ouvertes.fr/tel-00002224
Contributor : Mohammed El Rhabi <>
Submitted on : Monday, January 6, 2003 - 3:16:55 PM
Last modification on : Friday, May 29, 2020 - 3:59:08 PM
Long-term archiving on: : Friday, April 2, 2010 - 8:04:06 PM

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  • HAL Id : tel-00002224, version 1

Citation

Mohammed El Rhabi. Analyse Numérique et discrétisation par éléments spectraux avec joints des équations tridimensionnelles de l'électromagnétisme. Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2002. Français. ⟨tel-00002224⟩

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