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Détection numérique de petites imperfections de conductivité en 2D et 3D par une méthode dynamique basée sur l'équation des ondes et le contrôle géométrique

Abstract : In this thesis, we consider the numerical solution, in two- and three- dimensional bounded domains, of the inverse problem for identifying the location of small-volume, conductivity imperfections in a medium with homogeneous background. The identification of these inhomogeneities reposes on a dynamic approach based on the wave equation. Our numerical algorithm is based on the coupling of a finite element solution of the wave equation, an exact controllability method and finally a Fourier inversion for localizing the centers of the imperfections. A practical application of this procedure could be the determination of the location of anti-personnel mines or tumours. Numerical results, in two- and three-dimensions, show the robustness and accuracy of the approach for retrieving randomly placed imperfections from both complete and partial boundary measurements.
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https://tel.archives-ouvertes.fr/tel-00429530
Contributor : Jean-Baptiste Duval <>
Submitted on : Tuesday, November 3, 2009 - 12:09:12 PM
Last modification on : Thursday, January 11, 2018 - 6:12:26 AM
Long-term archiving on: : Tuesday, October 16, 2012 - 1:10:08 PM

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Jean-Baptiste Duval. Détection numérique de petites imperfections de conductivité en 2D et 3D par une méthode dynamique basée sur l'équation des ondes et le contrôle géométrique. Mathématiques [math]. Université de Picardie Jules Verne, 2009. Français. ⟨tel-00429530⟩

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