ON THE NUMERICAL-SOLUTION OF AN INVERSE BOUNDARY-VALUE PROBLEM FOR THE HEAT-EQUATION

We consider the inverse problem of reconstructing the interior boundar y curve of an arbitrary-shaped annulus from overdetermined Cauchy data on the exterior boundary curve. For the approximate solution of this ill-posed and nonlinear problem we propose a regularized Newton method based on a boundary integral equation approach for the initial bounda ry value problem for the heat equation. A theoretical foundation for t his Newton method is given by establishing the differentiability of th e initial boundary value problem with respect to the interior boundary curve in the sense of a domain derivative. Numerical examples indicat e the feasibility of our method.