Comptes Rendus
no. 7
Numerical Analysis/Mathematical Physics
Numerical approximation of a quantum drift-diffusion model
[Approximation numérique d'un modèle de dérive-diffusion quantique.]

Présenté par : Philippe G. Ciarlet

Samy Gallego1 ; Florian Méhats1
1 Mathématiques pour l'industrie et la physique (UMR 5640), université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse cedex 4, France
Comptes Rendus. Mathématique, Volume 339 (2004) no. 7, pp. 519-524.

Cette Note est consacrée à la discrétisation et à la simulation numérique d'un modèle de dérive-diffusion quantique qui a été dérivé récemment. Nous définissons un schéma numérique implicite dont la résolution se ramène à un problème de minimisation convexe. Par ailleurs, ce schéma préserve les propriétés physiques vérifiées par le modèle continu : conservation de la charge totale, positivité de la densité et dissipation d'une entropie. Enfin, nous illustrons ces propriétés à l'aide de simulations numériques.

This Note is devoted to the discretization and numerical simulation of a new quantum drift-diffusion model that was recently derived. We define an implicit numerical scheme which is equivalent to a convex minimization problem and which preserves the physical properties of the continuous model: charge conservation, positivity of the density and dissipation of an entropy. We illustrate these results by some numerical simulations.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2004.07.022
Samy Gallego 1 ; Florian Méhats 1

1 Mathématiques pour l'industrie et la physique (UMR 5640), université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse cedex 4, France 
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Samy Gallego; Florian Méhats. Numerical approximation of a quantum drift-diffusion model. Comptes Rendus. Mathématique, Volume 339 (2004) no. 7, pp. 519-524. doi : 10.1016/j.crma.2004.07.022. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.07.022/

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