Numerical reconstruction of a piecewise constant Robin parameter in the two- or three-dimensional case

Abstract

We are concerned with the inverse problem of identification of an unknown Robin parameter arising in the corrosion detection by electrostatic boundary measurements. First, the Robin inverse problem turns out to an optimization one by making use of the Kohn–Vogelius-like cost function J. Then, we prove differentiability of J with respect to the singularities surfaces of the Robin parameter, we propose a numerical algorithm of gradient type and we present several numerical tests for reconstructing a piecewise constant Robin parameter in both two- and three-dimensional cases.