We deal with an inverse scattering problem whose aim is to determine the thickness variation of a dielectric thin coating located on a conducting structure of unknown shape. The inverse scattering problem is solved through the application of the Generalized Impedance Boundary Conditions (GIBCs) which contain the thickness, curvature as well as material 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 uniqueness results for the inverse problem, the required total field as well as its higher order derivatives appearing in the GIBCs are obtained by the analytical continuation of the measured data to the coating surface through the single layer potential representation. The resulting system of non-linear differential equations for the unknown coating thickness is solved iteratively via the Newton-Raphson method after expanding the thickness function in a series of exponentials. Through the simulations it has been shown that the approach is effective under the validity conditions of the GIBCs.
Mots-clés : generalized impedance boundary conditions, thin coatings, inverse scattering problems, single layer potential, Newton−Raphson method
@article{M2AN_2014__48_4_1011_0,
author = {Aslany\"urek, Birol and Sahint\"urk, H\"ulya},
title = {Reconstruction of thickness variation of a dielectric coating through the generalized impedance boundary conditions},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1011--1027},
publisher = {EDP-Sciences},
volume = {48},
number = {4},
year = {2014},
doi = {10.1051/m2an/2013131},
mrnumber = {3264344},
zbl = {1297.78004},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an/2013131/}
}
TY - JOUR AU - Aslanyürek, Birol AU - Sahintürk, Hülya TI - Reconstruction of thickness variation of a dielectric coating through the generalized impedance boundary conditions JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2014 SP - 1011 EP - 1027 VL - 48 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2013131/ DO - 10.1051/m2an/2013131 LA - en ID - M2AN_2014__48_4_1011_0 ER -
%0 Journal Article %A Aslanyürek, Birol %A Sahintürk, Hülya %T Reconstruction of thickness variation of a dielectric coating through the generalized impedance boundary conditions %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2014 %P 1011-1027 %V 48 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2013131/ %R 10.1051/m2an/2013131 %G en %F M2AN_2014__48_4_1011_0
Aslanyürek, Birol; Sahintürk, Hülya. Reconstruction of thickness variation of a dielectric coating through the generalized impedance boundary conditions. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 4, pp. 1011-1027. doi : 10.1051/m2an/2013131. http://archive.numdam.org/articles/10.1051/m2an/2013131/
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