GPELab, a Matlab toolbox to solve Gross–Pitaevskii equations I: Computation of stationary solutions. This paper presents GPELab (Gross–Pitaevskii Equation Laboratory), an advanced easy-to-use and flexible Matlab toolbox for numerically simulating many complex physics situations related to Bose–Einstein condensation. The model equation that GPELab solves is the Gross–Pitaevskii equation. The aim of this first part is to present the physical problems and the robust and accurate numerical schemes that are implemented for computing stationary solutions, to show a few computational examples and to explain how the basic GPELab functions work. Problems that can be solved include: 1d, 2d and 3d situations, general potentials, large classes of local and nonlocal nonlinearities, multi-components problems, and fast rotating gases. The toolbox is developed in such a way that other physics applications that require the numerical solution of general Schrödinger-type equations can be considered.

References in zbMATH (referenced in 13 articles )

Showing results 1 to 13 of 13.
Sorted by year (citations)

  1. Antoine, Xavier; Levitt, Antoine; Tang, Qinglin: Efficient spectral computation of the stationary states of rotating Bose-Einstein condensates by preconditioned nonlinear conjugate gradient methods (2017)
  2. Antoine, X.; Lorin, E.: An analysis of Schwarz waveform relaxation domain decomposition methods for the imaginary-time linear Schrödinger and Gross-Pitaevskii equations (2017)
  3. Henning, Patrick; Peterseim, Daniel: Crank-Nicolson Galerkin approximations to nonlinear Schrödinger equations with rough potentials (2017)
  4. Wu, Xinming; Wen, Zaiwen; Bao, Weizhu: A regularized Newton method for computing ground states of Bose-Einstein condensates (2017)
  5. Antoine, Xavier; Besse, Christophe; Rispoli, Vittorio: High-order IMEX-spectral schemes for computing the dynamics of systems of nonlinear Schrödinger/Gross-Pitaevskii equations (2016)
  6. Antoine, Xavier; Tang, Qinglin; Zhang, Yong: On the ground states and dynamics of space fractional nonlinear Schrödinger/Gross-Pitaevskii equations with rotation term and nonlocal nonlinear interactions (2016)
  7. Correggi, M.; Dimonte, D.: On the third critical speed for rotating Bose-Einstein condensates (2016)
  8. Vergez, Guillaume; Danaila, Ionut; Auliac, Sylvain; Hecht, Frédéric: A finite-element toolbox for the stationary Gross-Pitaevskii equation with rotation (2016)
  9. Antoine, Xavier; Duboscq, Romain: Modeling and computation of Bose-Einstein condensates: stationary states, nucleation, dynamics, stochasticity (2015)
  10. Antoine, Xavier; Duboscq, Romain: GPELab, a Matlab toolbox to solve Gross-Pitaevskii equations. II: Dynamics and stochastic simulations (2015)
  11. Blanc, Xavier; Lewin, Mathieu: The crystallization conjecture: a review (2015)
  12. Antoine, Xavier; Duboscq, Romain: Robust and efficient preconditioned Krylov spectral solvers for computing the ground states of fast rotating and strongly interacting Bose-Einstein condensates (2014)
  13. Antoine, Xavier; Duboscq, Romain: GPELab, a Matlab toolbox to solve Gross-Pitaevskii equations. I: Computation of stationary solutions (2014)