The generalized impedance boundary conditions (GIBC’s) are used to model obstacles with corrugated
surfaces or obstacles with a thin layer of coating and they are often employed in simplifying the analytical solutions or reducing the cost of numerical computations for problems involving complex structures. We consider the reconstruction of surface impedance functions of a sound-soft three-dimensional obstacle coated with a thin layer of a penetrable material from few far field data at a fixed frequency. The technique we present is based on an iteratively regularized Newton-type method, which combines ideas of both iterative and decomposition methods. Employing a boundary integral equation approach the inverse problem is proved to be equivalent to a system of nonlinear integral equations. We illustrate the feasibility of the technique by numerical examples.
The proposed inversion algorithm is efficient from the computational point of view since the solutions of
boundary value problems appearing in the classical Newton iteration are replaced by matrix-vector products. Furthermore, it lays down the foundation to the reconstruction algorithm of surface impedances and shape of the coated obstacle simultaneously. In the concluding part of the talk we discuss the possibility of applying the method to inverse problems with GIBC for two-dimensional linear viscoelasticity.