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Numerical solution of an inverse initial boundary value problem forthe wave equation in the presenceof conductivity imperfections ofsmall volume

Published online by Cambridge University Press:  06 August 2010

Mark Asch ,
Marion Darbas  and
Jean-Baptiste Duval
Mark Asch
Affiliation:
LAMFA-CNRS UMR 6140, Université de Picardie Jules Verne, 80039 Amiens, France. [email protected]
Marion Darbas
Affiliation:
LAMFA-CNRS UMR 6140, Université de Picardie Jules Verne, 80039 Amiens, France. [email protected]
Jean-Baptiste Duval
Affiliation:
LAMFA-CNRS UMR 6140, Université de Picardie Jules Verne, 80039 Amiens, France. [email protected]
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Abstract

We consider the numerical solution, in two- and three-dimensionalbounded domains, of the inverse problem for identifying the locationof small-volume, conductivity imperfections in a medium with homogeneousbackground. A dynamic approach, based on the wave equation, permitsus to treat the important case of “limited-view” data. Our numericalalgorithm is based on the coupling of a finite element solution ofthe wave equation, an exact controllability method and finally a Fourierinversion for localizing the centers of the imperfections. Numericalresults, in 2- and 3-D, show the robustness and accuracy of the approachfor retrieving randomly placed imperfections from both complete andpartial boundary measurements.

Keywords

Wave equationexact controllabilityinverse problemfinite elementsFourier inversion
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 17 , Issue 4 , October 2011 , pp. 1016 - 1034
Copyright
© EDP Sciences, SMAI, 2010

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