Rodríguez Garcia, Jerónimo (2004) Space-time mesh refinement for elastodynamic equations. PhD thesis Mathématiques appliquées, Université Paris-Dauphine / ENSTA / UMA - Laboratoire de Mathématiques Appliquées, ?? institution/ensta ?? 2004PA090067.
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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.
| Item Type: | PhD Thesis (PhD) |
|---|---|
| Thesis Supervisor: | Joly, Patrick and Béache, Éliane |
| Date: | December 2004 |
| Board of examiners: | Piperno, Serge and Maday, Yvon and Després, Bruno and Séré, Éric |
| Ecole Doctorale: | ?? ED_408 ?? |
| Discipline: | Mathématiques appliquées |
| Collection (Fonds): | ?? fond/ensta ?? ?? fond/ensta ?? |
| Institution: | ?? institution/ensta ?? |
| Department: | Université Paris-Dauphine / ENSTA / UMA - Laboratoire de Mathématiques Appliquées |
| Subjects: | ?? math ?? ?? matmec ?? |
| Uncontrolled Keywords: | Mesh refinement, Local time stepping, Stability, Energy conservation, Fictitious domain method, Mixed finite elements, Error estimates, Wave propagation problems, Linear elastodynamics, Raffinement de maillage, Pas de temps local, Stabilité, Conservation d'énergie, Domaines fictifs, éléments finis mixtes, Estimation d'erreur, Propagation et diffraction d'ondes, élastodynamique linéaire |
| ID Code: | 2379 |
| Deposited By: | INVALID USER |
| Deposited On: | 23 April 2007 |
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