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Résolution numérique des équations de Maxwell harmoniques par une méthode d'éléments finis discontinus

Abstract : This work is devoted to the theoretic and numerical resolution of Maxwell equations in the time or frequency domain. In a first part, we prove that the time problem is well posed. We also deal with the asymptotic behavior of the solution when the right hand side of the equations is sinusoidal in time. In our approach we use the following tools: the theory of linear first order hyperbolic systems, the Hille-Yosida theorem, the limiting amplitude principle, the limiting absorption principle, and some trace theorems (in the boundary problem). Then, we develop a discontinuous finite elements method for the numerical resolution of the frequency problem, based on a flux splitting. This method is well adapted to unstructured meshes, and local refinements are simplified. An error estimate is proved. An iterative algorithm is then described to solve the discrete problem. It is based on a domain decomposition without covering. It is shown to be convergent towards the unique discrete solution, and it has been implemented on a parallel computer (IPSC 860). An integral equation is also built, for the resolution of the problem in an unbounded domain. Numerical experiments are described in the case of a piecewise constant approximation.
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https://tel.archives-ouvertes.fr/tel-00657828
Contributor : Philippe Helluy Connect in order to contact the contributor
Submitted on : Monday, January 9, 2012 - 1:19:27 PM
Last modification on : Monday, July 6, 2020 - 11:51:28 AM
Long-term archiving on: : Tuesday, April 10, 2012 - 2:30:52 AM

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  • HAL Id : tel-00657828, version 1

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Philippe Helluy. Résolution numérique des équations de Maxwell harmoniques par une méthode d'éléments finis discontinus. Analyse numérique [math.NA]. Ecole nationale superieure de l'aeronautique et de l'espace, 1994. Français. ⟨tel-00657828⟩

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