Abstract
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.
| Original language | English (US) |
|---|---|
| Title of host publication | Communications in Computational Physics |
| Publisher | Global Science Press |
| Pages | 1141-1166 |
| Number of pages | 26 |
| DOIs | |
| State | Published - May 17 2016 |
| Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2022-07-01Acknowledgements: We acknowledge support from the Ministry of Education of Singapore grant R-146-000-196-112 (W. Bao), the Natural Science Foundation of China grant No. 91430103 and the French ANR-12-MONU-0007-02 BECASIM (Q. Tang), the ANR project Moonrise ANR-14-CE23-0007-01 (Y. Zhang), and the Austrian Science Foundation (FWF) under grant No. F41 (project VICOM), grant No. I830 (project LODIQUAS) and the Austrian Ministry of Science and Research via its grant for the WPI (Q. Tang and Y. Zhang). The computation results presented have been achieved by using the Vienna Scientific Cluster. This work was partially done while the authors were visiting Beijing Computational Science Research Center in the summer of 2014, the Institute for Mathematical Sciences, National University of Singapore, in 2015, and the Computer, Electrical and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology, in 2014
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)