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“Robust and efficient preconditioned Krylov spectral solvers for computing the ground states of fast rotating and strongly interacting Bose-Einstein condensates”
Xavier Antoine and Romain Duboscq
Journal of Computational Physics, 2013

Abstract: We consider the Backward Euler SPectral (BESP) scheme proposed in [9] for computing the stationary states of Bose-Einstein Condensates (BECs) through the Gross-Pitaevskii equation. We show that the fixed point approach introduced in [9] fails to converge for fast rotating BECs. A simple alternative approach based on Krylov subspace solvers with a Laplace or Thomas-Fermi preconditioner is given. Numerical simulations (obtained with the associated freely available Matlab toolbox GPELab) for complex configurations show that the method is accurate, fast and robust for 2D/3D problems and multi-components BECs.

BibTex reference

@ARTICLE{AD2013,
   AUTHOR     = "Xavier Antoine and Romain Duboscq",
   TITLE      = "Robust and efficient preconditioned Krylov spectral solvers for compu
                   ting the ground states of fast rotating and strongly interacting Bose-
                   Einstein condensates",
   JOURNAL    = "Journal of Computational Physics",
   YEAR       = "2013",
}