Efficient time integration methods for Gross-Pitaevskii equations with rotation term

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type , Other ORP type 01 Jan 2019Embargo end date: 01 Oct 2019 Austria, Spain Publisher:American Institute of Mathematical Sciences (AIMS)Journal:Journal of Computational Dynamics, volume 6, pages 147-169 (issn: 2158-2491, eissn: 2158-2505,

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Authors: Bader, Philipp; Blanes, Sergio; Casas, Fernando; Thalhammer, Mechthild;

doi: 10.3934/jcd.2019008 , 10.48550/arxiv.1910.12097

arXiv: 1910.12097

handle: 10234/186831

Efficient time integration methods for Gross-Pitaevskii equations with rotation term

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Abstract

The objective of this work is the introduction and investigation of favourable time integration methods for the Gross--Pitaevskii equation with rotation term. Employing a reformulation in rotating Lagrangian coordinates, the equation takes the form of a nonlinear Schr{ö}dinger equation involving a space-time-dependent potential. A natural approach that combines commutator-free quasi-Magnus exponential integrators with operator splitting methods and Fourier spectral space discretisations is proposed. Furthermore, the special structure of the Hamilton operator permits the design of specifically tailored schemes. Numerical experiments confirm the good performance of the resulting exponential integrators.

24 pages, 13 figures

Countries

Austria, Spain

Related Organizations

Jaume I University
Spain
University of Innsbruck
Austria
Universitat Politècnica de València
Spain
Universitat Politècnica deValència
Spain
Universitat Politéncica de Valencia
Spain

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Keywords

commutator-free quasi-Magnus integrators, nonlinear Schrödinger equations, 65M70, 65L05, FOS: Physical sciences, Nonlinear Schrödinger equations, Exponential integrators, Gross-Pitaevskii equations, Fast Fourier transform, spectral methods, Magnus integrators, FOS: Mathematics, Mathematics - Numerical Analysis, Numerical methods for discrete and fast Fourier transforms, Quantum Physics, Commutator-free quasi-Magnus integrators, NLS equations (nonlinear Schrödinger equations), Numerical Analysis (math.NA), fast Fourier transform, Spectral methods, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, MATEMATICA APLICADA, Quantum Physics (quant-ph), Stability and convergence of numerical methods for ordinary differential equations, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs, exponential integrators

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