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In this paper, we propose an efficient and accurate numerical method forcomputing the ground state of spin-1 Bose-Einstein condensates (BEC) by usingthe normalized gradient flow or imaginary time method. The key idea is to finda third projection or normalization condition based on the relation between thechemical potentials so that the three projection parameters used in theprojection step of the normalized gradient flow are uniquely determined by thiscondition as well as the other two physical conditions given by theconservation of total mass and total magnetization. This allows us tosuccessfully extend the most popular and powerful normalized gradient flow orimaginary time method for computing the ground state of single component BEC tocompute the ground state of spin-1 BEC. An efficient and accuratediscretization scheme, the backward-forward Euler sine-pseudospectral method(BFSP), is proposed to discretize the normalized gradient flow. Extensivenumerical results on ground states of spin-1 BEC withferromagnetic/antiferromagnetic interaction and harmonic/optical latticepotential in one/three dimensions are reported to demonstrate the efficiency ofour new numerical method.

Computing Ground States of Spin-1 Bose-Einstein Condensates by the Normalized Gradient Flow