TY - JOUR
T1 - Accurate and Efficient Numerical Methods for Computing Ground States and Dynamics of Dipolar Bose-Einstein Condensates via the Nonuniform FFT
AU - Bao , Weizhu
AU - Tang , Qinglin
AU - Zhang , Yong
JO - Communications in Computational Physics
VL - 5
SP - 1141
EP - 1166
PY - 2019
DA - 2019/12
SN - 19
DO - http://doi.org/10.4208/cicp.scpde14.37s
UR - https://global-sci.org/intro/article_detail/cicp/13535.html
KW - Dipolar BEC, dipole-dipole interaction, NUFFT, ground state, dynamics, collapse.
AB - <p style="text-align: justify;">We propose efficient and accurate numerical methods for computing the
ground state and dynamics of the dipolar Bose-Einstein condensates utilising a
newly developed dipole-dipole interaction (DDI) solver that is implemented with the
non-uniform fast Fourier transform (NUFFT) algorithm. We begin with the three-dimensional (3D) Gross-Pitaevskii equation (GPE) with a DDI term and present the
corresponding two-dimensional (2D) model under a strongly anisotropic confining
potential. Different from existing methods, the NUFFT based DDI solver removes the
singularity by adopting the spherical/polar coordinates in the Fourier space in 3D/2D,
respectively, thus it can achieve spectral accuracy in space and simultaneously maintain high efficiency by making full use of FFT and NUFFT whenever it is necessary
and/or needed. Then, we incorporate this solver into existing successful methods for
computing the ground state and dynamics of GPE with a DDI for dipolar BEC. Extensive numerical comparisons with existing methods are carried out for computing the
DDI, ground states and dynamics of the dipolar BEC. Numerical results show that our
new methods outperform existing methods in terms of both accuracy and efficiency.</p>