The application of domain derivative for heat conduction with mixed condition in shape reconstruction

We consider the inverse problem for heat conduction with mixed condition to reconstruct the shape of multiple connected domain. A representation for domain derivative of the corresponding operator is established. This allows the investigation of the regularized iterative method for the solution of this ill-posed and nonlinear problem.The results of several numerical experiments show that the iterative algorithm gives good reconstruction, and indicate the feasibility of this method.