A comparison of the Landweber method and the Gauss–Newton method for an inverse parabolic boundary value problem

We consider an inverse boundary value problem for the heat equation that consists of the identification of the interior boundary curve of an annuli from given temperature and heat flux measurements on the exterior boundary. In order to solve the problem in a stable way, we apply the Landweber method, where we treat both the direct and the adjoint problem by means of the boundary integral equation method. Numerical examples, including a comparison to the Gauss–Newton method, are presented.