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Theses

Modélisation mathématique et simulation numérique avancée des phénomènes de propagation d'ondes dans les médias élastiques sans limite.

Abstract : Motivated by applications in geophysics and seismic engineering, this thesis seeks to contribute to the study of wave propagation phenomena in unbounded elastic media. Mathematical and numerical techniques are developed to solve time-harmonic scattering problems in exterior infinite and locally perturbed semi-infinite domains. In addition, we introduce a novel impedance boundary condition in elasticity, which generalizes the traction-free boundary condition usually considered to describe the ground surface in geophysical problems. The surface waves appearing with this boundary condition are investigated. We show the existence of the Rayleigh wave and how it depends on impedance. Moreover, we prove that an additional surface wave appears in a particular case. To deal numerically with unbounded domains, we consider approaches based upon exact boundary conditions and boundary integral equation methods. The former is applied to exterior domains, while the latter is employed in both types of unbounded domains. Special emphasis is placed on integral equations and boundary element methods to solve scattering problems in locally perturbed half-planes. The Green's function of the elastic half-plane with impedance boundary conditions is computed in an effective and accurate way, by employing a method of calculation that combines appropriately analytical and numerical techniques. A boundary integral equation method based on the calculated Green's function is then proposed. Finally, the numerical procedures are validated by employing appropriate benchmark problems.
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https://pastel.archives-ouvertes.fr/pastel-00006252
Contributor : Ecole Polytechnique <>
Submitted on : Sunday, July 18, 2010 - 8:00:00 AM
Last modification on : Wednesday, March 27, 2019 - 4:08:31 PM
Long-term archiving on: : Thursday, March 30, 2017 - 5:57:26 AM

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  • HAL Id : pastel-00006252, version 1

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Eduardo Godoy. Modélisation mathématique et simulation numérique avancée des phénomènes de propagation d'ondes dans les médias élastiques sans limite.. Mathématiques [math]. Ecole Polytechnique X, 2010. Français. ⟨pastel-00006252⟩

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