Numerical reconstruction of the first band(s) in an inverse Hill's problem - Archive ouverte HAL
Journal Articles ESAIM: Control, Optimisation and Calculus of Variations Year : 2020

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

Abstract

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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Dates and versions

hal-01591133 , version 1 (20-09-2017)

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Cite

Athmane Bakhta, Virginie Ehrlacher, David Gontier. Numerical reconstruction of the first band(s) in an inverse Hill's problem. ESAIM: Control, Optimisation and Calculus of Variations, 2020, ⟨10.1051/cocv/2019031⟩. ⟨hal-01591133⟩
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