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Numerical reconstruction of the first band(s) in an inverse Hill's problem

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inverse_problem_paper.pdf (814.2Kb)
Date
2017
Dewey
Analyse
Sujet
Inverse Hill; optimisation; inverse band structure; periodic Schrödinger operator
Journal issue
ESAIM: Control, Optimisation and Calculus of Variations
Publication date
2019
Publisher
edp sciences
DOI
http://dx.doi.org/doi.org/10.1051/cocv/2019031
Forthcoming
oui
URI
https://basepub.dauphine.fr/handle/123456789/19620
Collections
  • CEREMADE : Publications
Metadata
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Author
Ehrlacher, Virginie
51621 Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique [CERMICS]
Bakhta, Athmane
51621 Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique [CERMICS]
Gontier, David
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Article accepté pour publication ou publié
Abstract (EN)
This paper concerns an inverse band structure problem for one dimensional periodic Schrödinger operators (Hill's operators). Our goal is to find a potential for the Hill's operator in order to reproduce as best as possible some given target bands, which may not be realisable. We recast the problem as an optimisation problem, and prove that this problem is well-posed when considering singular potentials (Borel measures). We then propose different algorithms to tackle the problem numerically.

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