We deal with an inverse scattering problem whose aim is to determine the thicknessvariation of a dielectric thin coating located on a conducting structure of unknown shape.The inverse scattering problem is solved through the application of the GeneralizedImpedance Boundary Conditions (GIBCs) which contain the thickness, curvature as well asmaterial properties of the coating and they have been obtained in the previous work [B.Aslanyürek, H. Haddar and H.Şahintürk, Wave Motion 48 (2011)681–700] up to the third order with respect to the thickness. After proving uniquenessresults for the inverse problem, the required total field as well as its higher orderderivatives appearing in the GIBCs are obtained by the analytical continuation of themeasured data to the coating surface through the single layer potential representation.The resulting system of non-linear differential equations for the unknown coatingthickness is solved iteratively via the Newton−Raphson method after expanding thethickness function in a series of exponentials. Through the simulations it has been shownthat the approach is effective under the validity conditions of the GIBCs.

We analyze the accuracy and well-posedness of generalized impedanceboundary value problems in the framework of scattering problemsfrom unbounded highly absorbing media. We restrict ourselves in this first workto the scalar problem (E-mode for electromagnetic scattering problems). Compared to earlier works, the unboundedness of the rough absorbing layer introduces severe difficultiesin the analysis for the generalized impedance boundary conditions, sinceclassical compactness arguments are no longer possible. Our new analysisis based on the use of Rellich-type estimates and boundedness of L2solution operators. We also discuss some numerical experimentsconcerning these boundary conditions.

This paper addresses some results on the development of an approximate methodfor computing the acoustic field scattered by a three-dimensional penetrable object immersed into an incompressiblefluid. The basic idea of the method consists in using on-surface differentialoperators that locally reproduce the interior propagation phenomenon. This approach leads tointegral equation formulations with a reduced computational cost compared to standard integral formulations couplingboth the transmitted and scattered waves. Theoreticalaspects of the problem and numerical experiments are reported to analyze the efficiency ofthe method and precise its validity domain.