Numerical solution of an inverse initial boundary value problem for the wave equation in the presence of conductivity imperfections of small volume

LAMFA-CNRS UMR 6140, Université de Picardie Jules Verne, 80039 Amiens, France. mark.asch@u-picardie.fr

Received: 4 September 2009
Revised: 26 April 2010

Abstract

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.