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Asymptotic Models for an Elasto-Acoustic Problem with a Thin Layer

Victor Péron 1
1 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest
Abstract : Equivalent boundary Conditions have become a classic notion in the mathematical modeling of wave propagation phenomena. They are used for instance for scattering problems from thin obstacles. The general idea consist to replace an exact model inside the obstacle by approximate boundary conditions. This idea is pertinent if the Equivalent Condition (EC) can be easily handled numerically for instance when it is local. In this work we consider a 3D diffraction problem of elasto-acoustic waves in a solid medium surrounded by a thin layer of fluid medium. This problem is well suited for the notion of EC: due to the small thickness of the layer with respect to the wavelength, the effect of the fluid medium on the solid is as a first approximation local. This approach leads us to solve only elastic equations. The construction of ECs is based on a two-scale asymptotic expansion in power series of the thickness of the fluid layer. We study the mathematical models to ensure that the new conditions does not induce numerical instabilities. Questions regarding the implementation of the new conditions are addressed carefully in a joint work with Julien Diaz.
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Victor Péron. Asymptotic Models for an Elasto-Acoustic Problem with a Thin Layer. Twelfth International Conference Zaragoza-Pau on Mathematics, Sep 2012, Jaca, Spain. ⟨hal-00768042⟩

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