Reconstruction of the Electromagnetic Field in Layered Media Using the Concept of Approximate Transmission Conditions

Ozdemir, Özgür; Haddar, Houssem; Yaka, A.

doi:10.1109/tap.2011.2158967

Cited by 13 publications

(12 citation statements)

References 17 publications

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“…for j = 0, 1, 2..., and where again c := c(s) is the curvature of Γ 0 and conveying that U l = 0 for negative l. The recursive relations for the transmission conditions (2.4) and (2.5), and the partial differential equation (2.6) of the three lowest order terms U 0 , U 1 , U 2 allow us to derive relations between the jumps and mean values of the outer fields u 0 and u 1 and their co-normal derivatives across Γ 0 . In the following we summarize these relations (we refer the reader to ( [19]) and ( [29]) for details):…”

Section: 1mentioning

confidence: 99%

“…This introduces an essential computational difficulty in the numerical solution of the forward problem as well as in the solution of the corresponding inverse problem. In the following section we take advantage of the small scale of the thickness and, using an asymptotic method from [7,29], we derive an approximate model of the delaminated structure where the opening Ω 0 is replaced by new jump relations for u + and u − across the delaminated part Γ 0 that account for the presence of the opening. This is undertaken in Section 2 using formal asymptotic methods.…”

mentioning

confidence: 99%

“…Before analyzing the model further, we then demonstrate numerically that the asymptotic model predicts correctly the acoustic field and far field pattern of the scattered field for a particular model scatterer incorporating a delamination of small positive maximum width. Although there has been considerable work on the asymptotics of scattering from thin films (see for example [5,2,3,4,6,24,20,7,29]), the novelty of our reduced problem is that the delamination covers only a portion of the interface. The thickness of the delamination vanishes at its boundary and this introduces potential singularities into the asymptotic model.…”

mentioning

confidence: 99%

“…Hence, ξ = η δ and s are now the new coordinates inside Ω 0 . Next, following [7] and [29], we formally make the following ansatz for the fields U and…”

mentioning

confidence: 99%

“…Now based on the ansatz (2.1) and (2.3), and using the equations along with the transmission conditions, we can formally obtain an approximate model for the field in the opening Ω 0 . For detailed calculations we refer the reader to [19] (see also [29]) and in the following we simply sketch the steps that lead to our approximate model.…”

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confidence: 99%

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Nondestructive Testing of the Delaminated Interface between Two Materials

Cakoni¹,

Teresa²,

Haddar³

et al. 2016

SIAM J. Appl. Math.

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We consider the problem of detecting if two materials that should be in contact have separated or delaminated. The goal is to find an acoustic technique to detect the delamination. We model the delamination as a thin opening between two materials of different acoustic properties, and using asymptotic techniques we derive a asymptotic model where the delaminated region is replaced by jump conditions on the acoustic field and flux. The asymptotic model has potential singularities due to the edges of the delaminated region, and we show that the forward problem is well posed for a large class of possible delaminations. We then design a special Linear Sampling Method (LSM) for detecting the shape of the delamination assuming that the background, undamaged, state is known. Finally we show, by numerical experiments, that our LSM can indeed determine the shape of delaminated regions.

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Section: 1mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

“…Hence, ξ = η δ and s are now the new coordinates inside Ω 0 . Next, following [7] and [29], we formally make the following ansatz for the fields U and…”

mentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Nondestructive Testing of the Delaminated Interface between Two Materials

Cakoni¹,

Teresa²,

Haddar³

et al. 2016

SIAM J. Appl. Math.

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

Aslanyürek¹,

Şahintürk²

2014

ESAIM: M2AN

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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.

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An asymptotic model based on matching far and near field expansions for thin gratings problems

et al. 2021

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In this paper, we devise an asymptotic model for calculating electromagnetic diffraction and absorption in planar multilayered structures with a shallow surface-relief grating. Far from the grating, we assume that the solution can be written as a power series in terms of the grating thickness δ , the coefficients of this expansion being smooth up to the grating. However, the expansion approximates the solution only sufficiently far from the grating (far field approximation). Near the grating, we assume that there exists another expansion in powers of δ (near field approximation). Moreover, there is an overlapping zone where both expansion are valid. The proposed model is based on matching the two expansions on this overlapping domain. Then, by truncating terms of order δ 2 or higher, we obtain explicitly the equations satisfied by the lowest order terms in the power series. Under appropriate assumptions, we prove second order convergence of the error with respect to δ . Finally, an alternative form, more convenient for implementation, is derived and discretized with finite elements to perform some numerical tests.

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Reconstruction of the Electromagnetic Field in Layered Media Using the Concept of Approximate Transmission Conditions

Cited by 13 publications

References 17 publications

Nondestructive Testing of the Delaminated Interface between Two Materials

Nondestructive Testing of the Delaminated Interface between Two Materials

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

An asymptotic model based on matching far and near field expansions for thin gratings problems

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