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

Mark Asch (1) , Marion Darbas (1) , Jean-Baptiste Duval (1)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée

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.

Mots clés: Wave equation; exact controllability; inverse problem; finite elements; Fourier inversion

Domaines: Modélisation et simulation

Mark Asch, Marion Darbas, Jean-Baptiste Duval. 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, 2010, ⟨10.1051/cocv/2010031⟩. ⟨hal-00557302⟩