  In this paper, we design a novel class of arbitrarily high-order
structure-preserving numerical schemes for the time-dependent Gross-Pitaevskii
equation with angular momentum rotation in three dimensions. Based on the idea
of the scalar auxiliary variable approach which is proposed in the recent
papers [J. Comput. Phys., 416 (2018) 353-407 and SIAM Rev., 61(2019) 474-506]
for developing energy stable schemes for gradient flow systems, we firstly
reformulate the Gross-Pitaevskii equation into an equivalent system with a
modified energy conservation law. The reformulated system is then discretized
by the Gauss collocation method in time and the standard Fourier
pseudo-spectral method in space, respectively. We show that the proposed
schemes can preserve the discrete mass and modified energy exactly. Numerical
results are addressed to verify the efficiency and high-order accuracy of the
proposed schemes.
