International audienceWe consider the inverse obstacle scattering problem of determining both the shape and the "equiva- lent impedance" from far field measurements at a fixed frequency. In this work, the surface impedance is represented by a second order surface differential operator (refer to as generalized impedance boundary condition) as opposed to a scalar function. The generalized impedance boundary condition can be seen as a more accurate model for effective impedances and is widely used in the scattering problem for thin coatings. Our approach is based on a least square optimization technique. A major part of our analysis is to characterize the derivative of the cost function with respect to the boundary and this complex surface impedance configuration. In particular, we provide an extension of the notion of shape derivative to the case where the involved impedance parameters do not need to be surface traces of given functions, which leads (in general) to a non-vanishing tangential boundary perturbation. The efficiency of considering this type of derivative is illustrated by several 2D numerical experiments based on a (classical) steepest descent method. The feasibility of retrieving both the shape and the impedance parameters is also discussed in our numerical experiments

SubmittedInternational audienceWe analyze the factorization method (introduced by Kirsch in 1998 to solve inverse scattering problems at fixed frequency from the farfield operator) for a general class of boundary conditions that generalizes impedance boundary conditions. For instance, when the surface impedance operator is of pseudo-differential type, our main result stipulates that the factorization method works if the order of this operator is different from one and the operator is Fredholm of index zero with non negative imaginary part. We also provide some validating numerical examples for boundary operators of second order with discussion on the choice of the testing function

We are interested in the identification of a Generalized Impedance Boundary Condition from the far-fields created by one or several incident plane waves at a fixed frequency. We focus on the particular case where this boundary condition is expressed with the help of a second order surface operator: the inverse problem then amounts to retrieve the two functions λ and µ that define this boundary operator. We first derive a global Lipschitz stability result for the identification of λ or µ from the far-field for bounded piecewise constant impedance coefficients and we give a new type of stability estimate when inexact knowledge of the boundary is assumed. We then introduce an optimization method to identify λ and µ, using in particular a H 1 -type regularization of the gradient. We lastly show some numerical results in two dimensions, including a study of the impact of some various parameters, and by assuming either an exact knowledge of the shape of the obstacle or an approximate one.