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In this paper, we propose efficient and accurate numerical methods forcomputing the ground state and dynamics of the dipolar Bose-Einsteincondensates utilising a newly developed dipole-dipole interaction (DDI) solverthat 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) modelunder a strongly anisotropic confining potential. Different from existingmethods, the NUFFT based DDI solver removes the singularity by adopting thespherical/polar coordinates in Fourier space in 3D/2D, respectively, thus itcan achieve spectral accuracy in space and simultaneously maintain highefficiency by making full use of FFT and NUFFT whenever it is necessary and/orneeded. 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 forcomputing the DDI, ground states and dynamics of the dipolar BEC. Numericalresults show that our new methods outperform existing methods in terms of bothaccuracy and efficiency.

Accurate and efficient numerical methods for computing ground states and dynamics of dipolar Bose-Einstein condensates via the nonuniform FFT