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

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.