Asymptotic analysis of the scattering of a time-harmonic electromagnetic wave by a perfectly conducting metal coated with a thin dielectric shell

Bendali, Abderrahmane; Lemrabet, Keddour

doi:10.3233/asy-2008-0870

Cited by 19 publications

(10 citation statements)

References 19 publications

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“…Therefore, using again regularity results [3, Corollary 2.15], we deduce that E ∈ (H 1 (Ω R )) 3 . To obtain further regularity let us remark that similarly to equation (4) we have…”

Section: The Forward and Inverse Problems 21 The Generalized Impedanmentioning

confidence: 99%

“…The specificity of our work compared to the vast literature on inverse scattering problems [14], is to address coating models for which the impedance is written as a surface wave operator. They can also be referred to as generalized impedance boundary conditions [16,4]. They provide accurate models for thin dielectric coatings, imperfectly conducting obstacles or corrugated surfaces [17] and they can also be used as models for plasmonic waves [30].…”

Section: Introductionmentioning

confidence: 99%

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Electromagnetic inverse shape problem for coated obstacles

Chaulet

Haddar

2015

Adv Comput Math

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We address the inverse problem of retrieving the shape of an obstacle with impedance in the form of a surface wave operator using the knowledge of electromagnetic scattering amplitude at a fixed frequency. We prove unique reconstructions from infinitely many measures. We then provide a characterization of the scattering amplitude derivative with respect to the obstacle shape. This derivative includes the case of shape dependent impedance parameters. We then employ a gradientdescent algorithm with H 1 boundary regularisation of the descent direction to numerically solve the inverse problem. The procedure is validated for three dimensional geometries using synthetic data.

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“…Therefore, using again regularity results [3, Corollary 2.15], we deduce that E ∈ (H 1 (Ω R )) 3 . To obtain further regularity let us remark that similarly to equation (4) we have…”

Section: The Forward and Inverse Problems 21 The Generalized Impedanmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Electromagnetic inverse shape problem for coated obstacles

Chaulet

Haddar

2015

Adv Comput Math

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“…where R δl , Q δl and P δl are differential operators defined on the exterior surface of the thin coating and Q δl is an invertible elliptic operator. This approach is developed to overcome difficulties related to numerical instabilities in the context of a fourth order operator appearing in the third order approximation of the impedance (see Bendali et al [5]). The procedure consists in writing Maxwell's equation inside the thin coating in the form of abstract differential equations (see Sec.…”

Section: Construction Of the Approximate Impedance Operatormentioning

confidence: 99%

Approximate impedance for time-harmonic Maxwell's equations in a non planar domain with contrasted multi-thin layers

Goffi

Lemrabet

Arens

2020

Journal of Mathematical Analysis and Applications

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The aim of this paper is to give asymptotic models for the impedance of contrasted multi-thin layers for the harmonic Maxwell's equations. We start from a transmission problem which describes the scattering of electromagnetic waves by an obstacle covered with a thin coating (superposition of different thin layers of dielectric materials).We show how to model the effect of the thin coating by an impedance boundary conditions on the boundary of the propagation domain. To this end, we use a technique of abstract differential equations.

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“…We now rewrite the problem in a truncated domain (see [3][4][5] for a similar reduction) in order to get a uniform stability result with respect to δ. The latter is actually going to be useful for proving error estimates between u δ and the asymptotic expansion that is going to be built in the next sections.…”

Section: Problem Settingmentioning

confidence: 99%

“…The latter can be derived by studying the asymptotic behaviour, as δ → 0, of the total field u δ . The asymptotic behaviour of solutions to problems with thin layers has been addressed by many authors in the last decade (cf., e.g., [5,7,8,12,15,17,20,33]. .…”

Section: Introductionmentioning

confidence: 99%

Scattering of a scalar time-harmonic wave by a penetrable obstacle with a thin layer

Boutarene

Cocquet²

2015

Eur. J. Appl. Math

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This work looks at the asymptotic behaviour of the solution to the Helmholtz equation in a penetrable domain of $\mathbb{R}$3 with a thin layer of thickness δ which tends to 0. We use the method of multi-scale expansion to derive and justify an asymptotic expansion of the solution with respect to the thickness δ up to any order. We then provide approximate transmission conditions of order two defined on an interface located inside the thin layer, with accuracy up to O(δ2), which allow one to take into account the influence of the thin layer.

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Asymptotic analysis of the scattering of a time-harmonic electromagnetic wave by a perfectly conducting metal coated with a thin dielectric shell

Cited by 19 publications

References 19 publications

Electromagnetic inverse shape problem for coated obstacles

Electromagnetic inverse shape problem for coated obstacles

Approximate impedance for time-harmonic Maxwell's equations in a non planar domain with contrasted multi-thin layers

Scattering of a scalar time-harmonic wave by a penetrable obstacle with a thin layer

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