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Reconstruction of thickness variation of a dielectric coatingthrough 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 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.

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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