Efficient and spectrally accurate numerical methods for computing ground and first excited states in Bose–Einstein condensates

Modeling and Computation of Bose-Einstein Condensates: Stationary States, Nucleation, Dynamics, Stochasticity

“…In particular, we show that there is a great interest in considering the pseudo-spectral approximation rather than the finite difference scheme. A similar study has been conducted by Bao, Chern & Lim [21], for Ω = 0, where the authors show that BESP provides a spectral precision compared with BEFD.…”

“…An alternative solution consists in considering a matrix-free iterative method. A first approach, introduced by Bao et al [21] for non rotating GPEs, is based on stationary (fixed-point) methods. It has been next extended to rotating BEC by Zeng & Zhang [124].…”

“…and for a weak nonlinear interaction (for example | f (1)| ≤ 10), a suitable approximation [21] of the fundamental state of problem (21) is given by…”

Asymptotic estimates of the convergence of classical Schwarz waveform relaxation domain decomposition methods for two-dimensional stationary quantum waves

“…ground state and excited states, is a major question in quantum physics, most particularly for BECs. Such a problem corresponds [9,10,11,16,17,18,19] to computing a real number µ and a space dependent function φ which satisfies the equation…”

“…To numerically determine (µ, φ), a well-known method is the so-called imaginary time method [9,10,11,16,17,18,19,20,23] which is also designated as a Continuous Normalized Gradient Flow (CNGF) method in the Applied Mathematics literature. It consists in solving (1) in imaginary-time, i.e.…”