Fauqueux, Sandrine (2003) Eléments finis mixtes spectraux et couches absorbantes parfaitement adaptées pour la propagation d’ondes élastiques en régime transitoire. PhD thesis Mathématiques appliquées, Université Paris-Dauphine / ENSTA UMA / INRIA / CNRS UMR 2706 - POEMS Propagation des Ondes : Etude Mathematique et Simulation, ENSTA 2003PA090002 p.271.
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Official URL: http://tel.archives-ouvertes.fr/tel-00007445
Abstract
We consider the propagation of elastic waves in unbounded domains. A new formulation of the
linear elasticity system as an H (div)−L2 system enables us to use the “mixed spectral finite element
method”, This new method is based on the definition of new spaces of approximation and the use of
mass-lumping. It leads to an explicit scheme with reduced storage and provides the same solution as
the spectral finite element method. Then, we modelize unbounded domains by using Perfectly Matched Layers. Instabilities in the PML in the case of particular 2D elastic media are pointed out and investigated. The numerical method is validated and tested in the case of acoustic and elastic realistic models. A plane wave analysis gives results about numerical dispersion and shows that meshes adapted to the physical and geometrical properties of the media are more accurate than the others. Then, an extension of the method to fluid-solid coupling is introduced for 2D seismic propagation.
| Item Type: | PhD Thesis (PhD) |
|---|---|
| Thesis Supervisor: | Cohen, Gary |
| Date: | 06 February 2003 |
| Board of examiners: | Maday, Yvon and Halpern, Laurence and Monk, Peter and Joly, Patrick and Vilotte, Jean-Pierre |
| Ecole Doctorale: | ED 408 ECOLE DOCTORALE DECISION, INFORMATIQUE, MATHEMATIQUES, ORGANISATION (EDDIMO) |
| Discipline: | Mathématiques appliquées |
| Collection (Fonds): | ENSTA |
| Institution: | ENSTA |
| Department: | Université Paris-Dauphine / ENSTA UMA / INRIA / CNRS UMR 2706 - POEMS Propagation des Ondes : Etude Mathematique et Simulation |
| Subjects: | 1. Mathematics and Applications |
| Uncontrolled Keywords: | Elasticity, élastodynamique linéaire, Spectral element, éléments spectraux, Mass-lumping, Condensation de masse, Perfectly matched layers, Couche absorbante parfaitement adaptée, Plane wave analysis, Analyse par ondes planes |
| ID Code: | 2507 |
|---|---|
| Deposited By: | Julien Karachehayas |
| Deposited On: | 07 June 2007 |
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