Reconstruction of generalized impedance functions for 3D acoustic scattering

Highlights: • Employing an analogue of the Huygens' principle a system of nonlinear boundary integral equations is derived. • An iteratively regularized Newton-type method is developed. • Numerical implementation of the reconstruction method is described and its feasibility/limitations are demonstrated by numerical examples. • The study lays down the foundation to reconstruction algorithms for coated obstacles, i.e. recovery of impedances and shape of the obstacle. -- Abstract: We consider the inverse obstacle scattering problem of determining both of the surface impedance functions from far field measurements for a few incident plane waves at a fixed frequency. The reconstruction algorithm we propose is based on an iteratively regularized Newton-type method and nonlinear integral equations. The mathematical foundation of the method is presented and the feasibility is illustrated by numerical examples.