An asymptotic preserving scheme based on ...
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Article dans une revue scientifique: Article original
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Title :
An asymptotic preserving scheme based on a new formulation for NLS in the semiclassical limit
Author(s) :
Besse, Christophe [Auteur]
SImulations and Modeling for PArticles and Fluids [SIMPAF]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Carles, Rémi [Auteur]
Institut de Mathématiques et de Modélisation de Montpellier [I3M]
Méhats, Florian [Auteur]
Institut de Recherche Mathématique de Rennes [IRMAR]
Invariant Preserving SOlvers [IPSO]
SImulations and Modeling for PArticles and Fluids [SIMPAF]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Carles, Rémi [Auteur]
Institut de Mathématiques et de Modélisation de Montpellier [I3M]
Méhats, Florian [Auteur]
Institut de Recherche Mathématique de Rennes [IRMAR]
Invariant Preserving SOlvers [IPSO]
Journal title :
Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal
Pages :
1228-1260
Publisher :
Society for Industrial and Applied Mathematics
Publication date :
2013
ISSN :
1540-3459
HAL domain(s) :
Mathématiques [math]/Analyse numérique [math.NA]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
English abstract : [en]
We consider the semiclassical limit for the nonlinear Schrodinger equation. We introduce a phase/amplitude representation given by a system similar to the hydrodynamical formulation, whose novelty consists in including ...
Show more >We consider the semiclassical limit for the nonlinear Schrodinger equation. We introduce a phase/amplitude representation given by a system similar to the hydrodynamical formulation, whose novelty consists in including some asymptotically vanishing viscosity. We prove that the system is always locally well-posed in a class of Sobolev spaces, and globally well-posed for a fixed positive Planck constant in the one-dimensional case. We propose a second order numerical scheme which is asymptotic preserving. Before singularities appear in the limiting Euler equation, we recover the quadratic physical observables as well as the wave function with mesh size and time step independent of the Planck constant. This approach is also well suited to the linear Schrodinger equation.Show less >
Show more >We consider the semiclassical limit for the nonlinear Schrodinger equation. We introduce a phase/amplitude representation given by a system similar to the hydrodynamical formulation, whose novelty consists in including some asymptotically vanishing viscosity. We prove that the system is always locally well-posed in a class of Sobolev spaces, and globally well-posed for a fixed positive Planck constant in the one-dimensional case. We propose a second order numerical scheme which is asymptotic preserving. Before singularities appear in the limiting Euler equation, we recover the quadratic physical observables as well as the wave function with mesh size and time step independent of the Planck constant. This approach is also well suited to the linear Schrodinger equation.Show less >
Language :
Anglais
Peer reviewed article :
Oui
Audience :
Internationale
Popular science :
Non
ANR Project :
Comment :
34 pages, 31 (colored) figures
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Submission date :
2025-01-24T10:27:57Z
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