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

Abstract

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.Mathematics Subject Classification. 35R30, 35L05, 65M60.

Numerical Reconstruction of Small Perturbations in the Electromagnetic Coefficients of a Dielectric Material

“…This yields a constructive numerical method for the localization of electromagnetic defects in the material. Recently, this has been tested successfully in the context of the wave equation for retrieving small conductivity imperfections [10]. The aim of the present paper is to generalize the method to the second order Maxwell equations.…”