An energy-gap cost functional for cavities identification

Abstract

This paper aims to solve an ill-posed cavities identification problem governed by Laplace equation with overdetermined boundary data. We introduce a Dirichlet-Neumann misfit function and we rephrase the inverse problem into a shape optimization one. The obtained problem is solved by a steepest descent algorithm using the gradient information combined with the level set method. The efficiency and accuracy of this approach is illustrated by numerical results.