Finite volumes for the Gross-Pitaevskii equation
Document type :
Pré-publication ou Document de travail
Title :
Finite volumes for the Gross-Pitaevskii equation
Author(s) :
Chauleur, Quentin [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Laboratoire de Physique des Lasers, Atomes et Molécules - UMR 8523 [PhLAM]
Systèmes de particules et systèmes dynamiques [Paradyse]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Laboratoire de Physique des Lasers, Atomes et Molécules - UMR 8523 [PhLAM]
Systèmes de particules et systèmes dynamiques [Paradyse]
English keyword(s) :
Nonlinear Schrödinger equations
Lie-Trotter splitting
Finite-volume method
Convergence analysis
Quantum turbulence
Lie-Trotter splitting
Finite-volume method
Convergence analysis
Quantum turbulence
HAL domain(s) :
Mathématiques [math]/Analyse numérique [math.NA]
English abstract : [en]
We study the approximation by a Voronoi finite-volume scheme of the Gross-Pitaevskii equation with time-dependent potential in two and three dimensions. We perform an explicit splitting scheme for the time integration ...
Show more >We study the approximation by a Voronoi finite-volume scheme of the Gross-Pitaevskii equation with time-dependent potential in two and three dimensions. We perform an explicit splitting scheme for the time integration alongside a two-point flux approximation scheme in space. We rigorously analyze the error bounds relying on discrete uniform Sobolev inequalities. We also prove the convergence of the pseudo-vorticity of the wave function. We finally perform some numerical simulations to illustrate our theoretical results.Show less >
Show more >We study the approximation by a Voronoi finite-volume scheme of the Gross-Pitaevskii equation with time-dependent potential in two and three dimensions. We perform an explicit splitting scheme for the time integration alongside a two-point flux approximation scheme in space. We rigorously analyze the error bounds relying on discrete uniform Sobolev inequalities. We also prove the convergence of the pseudo-vorticity of the wave function. We finally perform some numerical simulations to illustrate our theoretical results.Show less >
Language :
Anglais
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