Title :

An asymptotic preserving scheme based on a new formulation for NLS in the semiclassical limit

Author(s) :

Besse, Christophe [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
SImulations and Modeling for PArticles and Fluids [SIMPAF]
Carles, Rémi [Auteur]
Institut de Mathématiques et de Modélisation de Montpellier [I3M]
Méhats, Florian [Auteur]
Invariant Preserving SOlvers [IPSO]
Institut de Recherche Mathématique de Rennes [IRMAR]

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]

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 >

Language :

Anglais

Popular science :

Non

ANR Project :

Régimes Asymptotiques pour l'équation de Schrödinger

Comment :

34 pages, 31 (colored) figures

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL