Ezziani, Abdelaâziz (2005) Mathematical and numerical modeling of wave propagation in viscoelastic and poroelastic Media. PhD thesis Mathématiques appliquées, Université Paris-Dauphine / ENSTA UMA / INRIA / CNRS UMR 2706 - POEMS Propagation des Ondes : Etude Mathematique et Simulation, ENSTA 2005PA090019 p.227.
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Official URL: http://tel.archives-ouvertes.fr/tel-00009179
Abstract
We are interested in the mathematical and numerical modeling of wave propagation in underground media. We present two propagation model: (i) a generalization of Zener's model for viscoelastic media, (ii) Biot's model for poroelastic media. For each model we achieve a mathematical analysis, In particular, an existence and uniqueness of solution and an energy decay result. For the numerical resolution we construct a method specific to each model, based on a variational approach, a mixed finite elements approximation in space and a finite difference in time. We prove for each scheme obtained, a result of discrete energy decay which provides a sufficient stability condition. To simulate the waves propagation in unbounded domains, we adapt the perfectly matched layers techniques to viscoelastic and poroelastic waves. Finally, we present various numerical validations of the developed methods.
| Item Type: | PhD Thesis (PhD) |
|---|---|
| Thesis Supervisor: | Joly, Patrick and Bécache, Eliane |
| Date: | 08 February 2005 |
| Board of examiners: | Schatzman, Michelle and Chavent, Guy and Hazard, Christophe and Symes, William W. and Mulder, Wim and De Roeck, Yann Hervé |
| 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: | Poroelastic waves, Ondes poroélastiques, Viscoelastic waves, Ondes viscoélastiques, Mixed finite element, éléments finis mixtes, Mass lumping, Condensation de masse, Finite difference, Différences finies, Stability analysis, Analyse de stabilité, Energy, énergie |
| ID Code: | 2508 |
| Deposited By: | Julien Karachehayas |
| Deposited On: | 07 June 2007 |
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