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Approximation de haute précision des problèmes de diffraction.

Abstract : This work is about the high-accuracy study of waves diffracted by a bounded obstacle. Two aspects are considered : the reduction of the computational domain thanks to fictive absorbing media and the research of a new high-order explicit approximation whose stability is independent of the order of spatial approximation chosen. First, we consider the reduction of the computational domain by the Perfectly Matched Layers (PML) around non necessarily convex domains sets (but typical of scattering problems, meaning no trapping). Exhaustion domains diffeomorphic to convex are considered with almost necessary hypotheses. For Maxwell or waves equations, the existence and uniqueness are demonstrated in all the space and in artificially bounded domains, for both harmonic and unsteady problems. The decay is analyzed locally and asymptotically, and some numerical simulations are performed. The second part of the work is an alternative to the Discontinuous Galerkin methods, inspired by the J. Rauch regularity results. Its advantage is to preserve a CFL condition, such as the one for the Finite Volumes methods, independently of the order of approximation, for structured meshes as well as for unstructured ones. The convergence of this method is proven through consistancy and stability, thanks to the Lax-Richtmyer theorem, for structured meshes. For unstructured ones, the consistancy can no longer be established by the Taylor formula, so convergence is not guaranteed anymore, but the first bidimensional numerical experiments give excellent results.
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https://tel.archives-ouvertes.fr/tel-00475286
Contributor : Sophie Laurens <>
Submitted on : Wednesday, April 21, 2010 - 5:41:39 PM
Last modification on : Thursday, March 5, 2020 - 5:57:01 PM
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  • HAL Id : tel-00475286, version 2

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Sophie Laurens. Approximation de haute précision des problèmes de diffraction.. Mathématiques [math]. Université Paul Sabatier - Toulouse III, 2010. Français. ⟨tel-00475286v2⟩

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