An Asymptotic Preserving Scheme Based on a New Formulation for NLS in the Semiclassical Limit

DOI10.1137/120899017zbMath1291.35333arXiv1211.3391OpenAlexW3103100710MaRDI QIDQ5411177

Florian Méhats, Rémi Carles, Christophe Besse

Publication date: 22 April 2014

Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.3391

zbMATH Keywords

nonlinear Schrödinger equationnumerical simulationsemiclassical limitasymptotic preservingMadelung transform

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Statistical mechanics of superfluids (82D50) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Quantum hydrodynamics and relativistic hydrodynamics (76Y05) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Foundations of fluid mechanics (76A02) Euler equations (35Q31)

Related Items (8)

Computing quantum dynamics in the semiclassical regime ⋮ Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations ⋮ Asymptotic-preserving methods and multiscale models for plasma physics ⋮ Analysis of a splitting scheme for a class of random nonlinear partial differential equations ⋮ Efficient exponential splitting spectral methods for linear Schrödinger equation in the semiclassical regime ⋮ On Fourier time-splitting methods for nonlinear Schrödinger equations in the semi-classical limit. II. Analytic regularity ⋮ Uniformly accurate time-splitting methods for the semiclassical linear Schrödinger equation ⋮ High Order Exponential Integrators for Nonlinear Schrödinger Equations with Application to Rotating Bose--Einstein Condensates

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