2013/07/22 by Laurent Bourgeois, Bourgeois, Laurent, Nicolas Chaulet +3
Engineering · Mathematics · #Composite Material Mechanics #FOS: Mathematics #Microwave Imaging and Scattering Analysis #Numerical Analysis (math.NA) #Numerical methods in inverse problems
paper · doi:10.48550/arxiv.1307.5746
openalex publication_date 2013/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \ld 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 H1-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.