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

We consider the Backward Euler SPectral (BESP) scheme proposed in [8] for computing the stationary states of Bose-Einstein Condensates (BECs) through the Gross-Pitaevskii equation. We show that the fixed point approach introduced in [8] 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. An extension is provided when one wants to compute the dynamics of a BEC by adapting the relaxation scheme in [13].