Accurate and Efficient Numerical Methods for Computing Ground States and Dynamics of Dipolar Bose-Einstein Condensates via the Nonuniform FFT (Communications in Computational Physics, 2020)
We propose efficient and accurate numerical methods for computing theground state and dynamics of the dipolar Bose-Einstein condensates utilising anewly developed dipole-dipole interaction (DDI) solver that is implemented with thenon-uniform fast Fourier transform (NUFFT) algorithm. We begin with the three-dimensional (3D) Gross-Pitaevskii equation (GPE) with a DDI term and present thecorresponding two-dimensional (2D) model under a strongly anisotropic confiningpotential. Different from existing methods, the NUFFT based DDI solver removes thesingularity 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 necessaryand/or needed. Then, we incorporate this solver into existing successful methods forcomputing the ground state and dynamics of GPE with a DDI for dipolar BEC. Extensive numerical comparisons with existing methods are carried out for computing theDDI, ground states and dynamics of the dipolar BEC. Numerical results show that ournew methods outperform existing methods in terms of both accuracy and efficiency.