Robust and efficient preconditioned Krylov spectral solvers for computing the ground states of fast rotating and strongly interacting Bose-Einstein condensates

Xavier Antoine (1, 2, 3) , Romain Duboscq (1, 3)

1 CORIDA - Robust control of infinite dimensional systems and applications
2 ALICE - Geometry and Lighting
3 IECL - Institut Élie Cartan de Lorraine

We consider the Backward Euler SPectral (BESP) scheme proposed in [10] for computing the stationary states of Bose-Einstein Condensates (BECs) through the Gross-Pitaevskii equation. We show that the fixed point approach introduced in [10] 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.

Domaines: Analyse numérique [math.NA]

Xavier Antoine, Romain Duboscq. Robust and efficient preconditioned Krylov spectral solvers for computing the ground states of fast rotating and strongly interacting Bose-Einstein condensates. Journal of Computational Physics, 2014, 258 (1), pp.509-523. ⟨10.1016/j.jcp.2013.10.045⟩. ⟨hal-00931117⟩