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. A dynamic approach, based on the wave equation, permits us to treat the important case of “limited-view” data. 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. Numerical results, in 2- and 3-D, show the robustness and accuracy of the approach for retrieving randomly placed imperfections from both complete and partial boundary measurements.

Classification: 35R30, 35L05, 65M60

Keywords: wave equation, exact controllability, inverse problem, finite elements, Fourier inversion

@article{COCV_2011__17_4_1016_0, author = {Asch, Mark and Darbas, Marion and Duval, Jean-Baptiste}, title = {Numerical solution of an inverse initial boundary value problem for the wave equation in the presence of conductivity imperfections of small volume}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, publisher = {EDP-Sciences}, volume = {17}, number = {4}, year = {2011}, pages = {1016-1034}, doi = {10.1051/cocv/2010031}, zbl = {1254.35238}, mrnumber = {2859863}, language = {en}, url = {http://www.numdam.org/item/COCV_2011__17_4_1016_0} }

Asch, Mark; Darbas, Marion; Duval, Jean-Baptiste. Numerical solution of an inverse initial boundary value problem for the wave equation in the presence of conductivity imperfections of small volume. ESAIM: Control, Optimisation and Calculus of Variations, Volume 17 (2011) no. 4, pp. 1016-1034. doi : 10.1051/cocv/2010031. http://www.numdam.org/item/COCV_2011__17_4_1016_0/

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