Numerical Shape Reconstruction for a Semi-Linear Elliptic Interface Inverse Problem

Abstract

We consider a shape reconstruction inverse problem constrained by a semi-linear elliptic interface problem in reaction diffusion. The existence of the model is shown. We perform shape sensitivity analysis and propose two numerical optimization algorithms based on the distributed shape gradient. The first algorithm allows shape changes and the second algorithm uses a level set method allowing shape and topological changes. Numerical results are presented to verify effectiveness of the algorithms.