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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.
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},
pages = {1016--1034},
publisher = {EDP-Sciences},
volume = {17},
number = {4},
year = {2011},
doi = {10.1051/cocv/2010031},
mrnumber = {2859863},
zbl = {1254.35238},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2010031/}
}
TY - JOUR AU - Asch, Mark AU - Darbas, Marion AU - Duval, Jean-Baptiste TI - Numerical solution of an inverse initial boundary value problem for the wave equation in the presence of conductivity imperfections of small volume JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2011 SP - 1016 EP - 1034 VL - 17 IS - 4 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2010031/ DO - 10.1051/cocv/2010031 LA - en ID - COCV_2011__17_4_1016_0 ER -
%0 Journal Article %A Asch, Mark %A Darbas, Marion %A Duval, Jean-Baptiste %T Numerical solution of an inverse initial boundary value problem for the wave equation in the presence of conductivity imperfections of small volume %J ESAIM: Control, Optimisation and Calculus of Variations %D 2011 %P 1016-1034 %V 17 %N 4 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2010031/ %R 10.1051/cocv/2010031 %G en %F 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, Tome 17 (2011) no. 4, pp. 1016-1034. doi: 10.1051/cocv/2010031
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