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On uniqueness in electromagnetic scattering from biperiodic structures

Armin Lechleiter; Dinh-Liem Nguyen

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2013)

  • Volume: 47, Issue: 4, page 1167-1184
  • ISSN: 0764-583X

Abstract

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Consider time-harmonic electromagnetic wave scattering from a biperiodic dielectric structure mounted on a perfectly conducting plate in three dimensions. Given that uniqueness of solution holds, existence of solution follows from a well-known Fredholm framework for the variational formulation of the problem in a suitable Sobolev space. In this paper, we derive a Rellich identity for a solution to this variational problem under suitable smoothness conditions on the material parameter. Under additional non-trapping assumptions on the material parameter, this identity allows us to establish uniqueness of solution for all positive wave numbers.

How to cite

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Lechleiter, Armin, and Nguyen, Dinh-Liem. "On uniqueness in electromagnetic scattering from biperiodic structures." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 47.4 (2013): 1167-1184. <http://eudml.org/doc/273267>.

@article{Lechleiter2013,
abstract = {Consider time-harmonic electromagnetic wave scattering from a biperiodic dielectric structure mounted on a perfectly conducting plate in three dimensions. Given that uniqueness of solution holds, existence of solution follows from a well-known Fredholm framework for the variational formulation of the problem in a suitable Sobolev space. In this paper, we derive a Rellich identity for a solution to this variational problem under suitable smoothness conditions on the material parameter. Under additional non-trapping assumptions on the material parameter, this identity allows us to establish uniqueness of solution for all positive wave numbers.},
author = {Lechleiter, Armin, Nguyen, Dinh-Liem},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {biperiodic scattering; uniqueness; electromagnetic waves; electromagnetic scattering; biperiodic dielectric structure, variational formulation; Rellich identity},
language = {eng},
number = {4},
pages = {1167-1184},
publisher = {EDP-Sciences},
title = {On uniqueness in electromagnetic scattering from biperiodic structures},
url = {http://eudml.org/doc/273267},
volume = {47},
year = {2013},
}

TY - JOUR
AU - Lechleiter, Armin
AU - Nguyen, Dinh-Liem
TI - On uniqueness in electromagnetic scattering from biperiodic structures
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2013
PB - EDP-Sciences
VL - 47
IS - 4
SP - 1167
EP - 1184
AB - Consider time-harmonic electromagnetic wave scattering from a biperiodic dielectric structure mounted on a perfectly conducting plate in three dimensions. Given that uniqueness of solution holds, existence of solution follows from a well-known Fredholm framework for the variational formulation of the problem in a suitable Sobolev space. In this paper, we derive a Rellich identity for a solution to this variational problem under suitable smoothness conditions on the material parameter. Under additional non-trapping assumptions on the material parameter, this identity allows us to establish uniqueness of solution for all positive wave numbers.
LA - eng
KW - biperiodic scattering; uniqueness; electromagnetic waves; electromagnetic scattering; biperiodic dielectric structure, variational formulation; Rellich identity
UR - http://eudml.org/doc/273267
ER -

References

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  12. [12] H. Haddar and A. Lechleiter, Electromagnetic wave scattering from rough penetrable layers. SIAM J. Math. Anal.43 (2011) 2418–2433. Zbl1233.35182MR2861668
  13. [13] W. McLean, Strongly Elliptic Systems and Boundary Integral Operators. Cambridge University Press, Cambridge, UK (2000). Zbl0948.35001MR1742312
  14. [14] P. Monk, Finite Element Methods for Maxwell’s Equations. Oxford Science Publications, Oxford (2003). Zbl1024.78009
  15. [15] F. Rellich, Darstellung der Eigenwerte von Δu + λu = 0 durch ein Randintegral. Math. Zeitschrift 46 (1940) 635–636. Doi: 10.1007/BF01181459. Zbl0023.04204MR2456JFM66.0460.01
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