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An asymptotic representation formula for scattering by thin tubular structures and an application in inverse scattering

Capdeboscq, Yves; Griesmaier, Roland; Knöller, Marvin

Abstract:
We consider the scattering of time-harmonic electromagnetic waves by a penetrable thin tubular scattering object in three-dimensional free space. We establish an asymptotic representation formula for the scattered wave away from the thin tubular scatterer as the radius of its cross-section tends to zero. The shape, the relative electric permeability and the relative magnetic permittivity of the scattering object enter this asymptotic representation formula by means of the center curve of the thin tubular scatterer and two electric and magnetic polarization tensors. We give an explicit characterization of these two three-dimensional polarization tensors in terms of the center curve and of the two two-dimensional polarization tensor for the cross-section of the scattering object. As an application we demonstrate how this formula may be used to evaluate the residual and the shape derivative in an efficient iterative reconstruction algorithm for an inverse scattering problem with thin tubular scattering objects. We present numerical results to illustrate our theoretical findings.

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Volltext §
DOI: 10.5445/IR/1000124274
Veröffentlicht am 07.10.2020
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 09.2020
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000124274
Verlag KIT, Karlsruhe
Umfang 37 S.
Serie CRC Preprint ; 2020/25
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter electromagnetic scattering, Maxwell’s equations, thin tubular object, asymptotic analysis, polarization tensor, inverse scattering
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