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

Abstract

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 (Ochs et al., 2014), 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.