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 which consists of determining an unknown inner boundary of an annular domain and surface heat transfer coefficient 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. Numerical experiments are presented for the reconstruction algorithms, which show that both the shape and the surface impedance can be reconstructed accurately. AMS Mathematics Subject Classification 2010: 65N20,65N21.