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Raffinement de Maillage Spatio-Temporel pour les Équations de l'Élastodynamique

Jerónimo Rodríguez 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
CNRS - Centre National de la Recherche Scientifique : UMR7231, UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France
Abstract : This work deals with the simulation of wave scattering in elastic, anisotropic and heterogeneous media with cracks using explicit schemes. Our goal is the development of an efficient numerical method to capture the geometrical details or the singularities of the solution in an accurate way. In the first two parts we present space-time mesh refinement methods. Adapting the time step locally to the spatial discretization allows us to diminish the CPU time and the numerical dispersion on the coarse grid. These methods are conservative, a property that ensures the stability of the numerical scheme. The cracks are taken into account using the fictitious domain method. In the third part of this work we present a new mixed finite element that ensures the convergence of this method. Finally, the last part describes the coupling between conservative space-time mesh refinement techniques and the fictitious domain method.
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Submitted on : Monday, March 27, 2006 - 1:24:26 PM
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Jerónimo Rodríguez. Raffinement de Maillage Spatio-Temporel pour les Équations de l'Élastodynamique. Modélisation et simulation. Université Paris Dauphine - Paris IX, 2004. Français. ⟨tel-00012034v2⟩

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