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Reconstruction of thickness variation of a dielectric coating through the generalized impedance boundary conditions∗

Published online by Cambridge University Press:  30 June 2014

Birol Aslanyürek  and
Hülya Sahintürk
Birol Aslanyürek
Affiliation:
Mathematical Engineering, Yildiz Technical University, Davutpasa, 34220 Istanbul, Turkey. birolaslanyurek@yildiz.edu.tr; hsahin@yildiz.edu.tr
Hülya Sahintürk
Affiliation:
Mathematical Engineering, Yildiz Technical University, Davutpasa, 34220 Istanbul, Turkey. birolaslanyurek@yildiz.edu.tr; hsahin@yildiz.edu.tr
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Abstract

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.

Keywords

Generalized impedance boundary conditionsthin coatingsinverse scattering problemssingle layer potentialNewton−Raphson method
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 48 , Issue 4 , July 2014 , pp. 1011 - 1027
Copyright
© EDP Sciences, SMAI, 2014

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