Numerical reconstruction of an inhomogeneity in an elliptic equation

In this paper, the inverse problem which consists of reconstructing an unknown inner boundary of a domain from a single pair of boundary Cauchy data associated to an elliptic equation is solved numerically using the meshless method of fundamental solutions. A nonlinear minimization of the objective function is regularized. The stability of the numerical results is investigated for several test examples with respect to noise in the input data and various values of the regularization parameters.