Simultaneous reconstruction of the shape and surface impedance from Cauchy data for the Helmholtz equation

In this paper, we are concerned with the coefficients identification for the Helmholtz equation. This problem consists of determining the shape and surface impedance from boundary Cauchy data. We propose two reconstruction algorithms to simultaneously recover the shape and the surface impedance of the obstacle within a body. This problem is ill-posed, thus we apply regularization techniques in order to improve the corresponding approximation. The numerical results show that the proposed algorithms are stable and effective.