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

Birol Aslanyürek; Hülya Sahintürk

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2014)

  • Volume: 48, Issue: 4, page 1011-1027
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Aslanyürek, Birol, and Sahintürk, Hülya. "Reconstruction of thickness variation of a dielectric coating through the generalized impedance boundary conditions." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 48.4 (2014): 1011-1027. <http://eudml.org/doc/273262>.

@article{Aslanyürek2014,
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.},
author = {Aslanyürek, Birol, Sahintürk, Hülya},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {generalized impedance boundary conditions; thin coatings; inverse scattering problems; single layer potential; Newton−Raphson method; Newton-Raphson method},
language = {eng},
number = {4},
pages = {1011-1027},
publisher = {EDP-Sciences},
title = {Reconstruction of thickness variation of a dielectric coating through the generalized impedance boundary conditions},
url = {http://eudml.org/doc/273262},
volume = {48},
year = {2014},
}

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 - Modélisation Mathématique et Analyse Numérique
PY - 2014
PB - EDP-Sciences
VL - 48
IS - 4
SP - 1011
EP - 1027
AB - 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.
LA - eng
KW - generalized impedance boundary conditions; thin coatings; inverse scattering problems; single layer potential; Newton−Raphson method; Newton-Raphson method
UR - http://eudml.org/doc/273262
ER -

References

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