
Numerical reconstruction of the first band(s) in an inverse Hill's problem
Bakhta , Athmane; Ehrlacher, Virginie; Gontier, David (2020), Numerical reconstruction of the first band(s) in an inverse Hill's problem, ESAIM. Control, Optimisation and Calculus of Variations, 26, 59. 10.1051/cocv/2019031
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Article accepté pour publication ou publiéDate
2020Journal name
ESAIM. Control, Optimisation and Calculus of VariationsVolume
26Number
59Publisher
EDP Sciences
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Bakhta , AthmaneÉcole des Ponts ParisTech [ENPC]
Ehrlacher, Virginie
École des Ponts ParisTech [ENPC]
Gontier, David
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
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.Subjects / Keywords
Inverse Hill; optimisation; inverse band structure; periodic Schrödinger operatorRelated items
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