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Résolution des équations intégrales pour la diffraction d'ondes acoustiques et électromagnétiques - Stabilisation d'algorithmes itératifs et aspects de l'analyse numérique

Abstract : This thesis deals with the numerical solution of acoustic and electromagnetic time-harmonic scattering problems, by the boundary integral equation method. The Galerkin method with (scalar or vector) surface finite elements leads to ill-conditioned linear
systems of equations. In the first part, in order to enhance the convergence of iterative solvers we propose and study theoretically and numerically preconditioners based on Calderon formulas, which link the involved integral operators. In electromagnetism we also use discrete analogues of the Helmholtz decomposition of tangent fields to construct stable discretizations of the operators. In the second part we use estimates on such decompositions to provide a new numerical analysis of the electric field integral equation. This analysis is extended to open surfaces (screens), modeling thin perfect conductors.
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https://pastel.archives-ouvertes.fr/tel-00004520
Contributor : Snorre H. Christiansen <>
Submitted on : Thursday, February 5, 2004 - 3:06:56 PM
Last modification on : Friday, January 10, 2020 - 3:42:10 PM
Long-term archiving on: : Wednesday, September 12, 2012 - 1:10:18 PM

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  • HAL Id : tel-00004520, version 1

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Snorre H. Christiansen. Résolution des équations intégrales pour la diffraction d'ondes acoustiques et électromagnétiques - Stabilisation d'algorithmes itératifs et aspects de l'analyse numérique. Mathématiques [math]. Ecole Polytechnique X, 2002. Français. ⟨tel-00004520⟩

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