Numerical identification for impedance coefficient by a MFS-based optimization method

In this paper, we propose a new numerical method to solve an inverse impedance problem for Laplace's equation. The Robin coefficient in the impedance boundary condition is recovered from Cauchy data on a part of boundary. A crucial step is to transform the problem into an optimization problem based on the MFS and Tikhonov regularization. Then the popular conjugate gradient method is used to solve the minimization problem. We compare several stopping rules in the iteration procedure and try to find an accurate and stable approximation. Numerical results for four examples in 2D and 3D cases will show the effectiveness of the proposed method.