Acceleration of the imaginary time method for spectrally computing the stationary states of Gross-Pitaevskii equations

Xavier Antoine (1, 2) , Christophe Besse (3) , Romain Duboscq (3, 4) , Vittorio Rispoli (3)

1 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization
2 IECL - Institut Élie Cartan de Lorraine
3 IMT - Institut de Mathématiques de Toulouse UMR5219
4 INSA Toulouse - Institut National des Sciences Appliquées - Toulouse

The aim of this paper is to propose a simple accelerated spectral gradient flow formulation for solving the Gross-Pitaevskii Equation (GPE) when computing the stationary states of Bose-Einstein Condensates. The new algorithm, based on the recent iPiano minimization algorithm [35], converges three to four times faster than the standard implicit gradient scheme. To support the method, we provide a complete numerical study for 1d-2d-3d GPEs, including rotation and dipolar terms.

Mots clés: rotating Gross-Pitaevskii equation; imaginary time formulation; stationary states; Bose-Einstein condensation; accelerated gradient; pseudospectral approximation

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Xavier Antoine, Christophe Besse, Romain Duboscq, Vittorio Rispoli. Acceleration of the imaginary time method for spectrally computing the stationary states of Gross-Pitaevskii equations. Computer Physics Communications, 2017, 219, pp.70-78. ⟨10.1016/j.cpc.2017.05.008⟩. ⟨hal-01356227⟩