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Etude de schemas numeriques pour des modeles de propagation d'ondes en milieux heterogenes

Abstract : Least square inversion methods require wave propagation modeling by linear equations. It is in modeling that the main part of this work, which includes four chapters, has been done. In the first chapter we start with the inversion of a locally disturbed medium that is to say we look for an heterogeneity of given shape in an homogeneous matrix. We show in this simple case the influence of the source on the non-linearity of the cost function. In the second chapter we introduce and analyze a family of numerical schemes for the acoustic wave equation in homogeneous media. These schemes are of order two or four in time and of any order in space. We estimate the computational cost of modeling and advice a choice for the number of points per wavelength and points per period, which then yield the space and time steps. In the third chapter we study the stability and accuracy of this family of numerical schemes in heterogeneous media. We obtain stability results for arbitrary heterogeneous media and give the order of approximation of these schemes in heterogeneous media. We also study the sponge boundary condition. In the last chapter, we deal with a posteriori estimates for the wave equation in uni-dimensional media. These estimates can be extended to two dimensional media. They allow a measure of the error on the the solution by computable quantities which in turn provides guidance for time and space discretization in an adaptative procedure.
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https://theses.hal.science/tel-00584224
Contributor : Alain Sei Connect in order to contact the contributor
Submitted on : Thursday, April 7, 2011 - 5:44:39 PM
Last modification on : Tuesday, January 18, 2022 - 3:23:51 PM
Long-term archiving on: : Friday, July 8, 2011 - 2:59:28 AM

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  • HAL Id : tel-00584224, version 1

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Alain Sei. Etude de schemas numeriques pour des modeles de propagation d'ondes en milieux heterogenes. Modélisation et simulation. Université Paris Dauphine - Paris IX, 1991. Français. ⟨NNT : ⟩. ⟨tel-00584224⟩

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