A preconditioned Riemannian conjugate gradient method to compute ground states of Spin-1 Bose-Einstein condensates
Authors
Wen Huang, Zilin Yang, and Qinglin Tang
Abstract
In this paper, we propose a preconditioned Riemannian conjugate gradient method for computing ground states of spin-1 Bose-Einstein condensates, which can be reformulated as an optimization problem with the mass and magnetization constraints. The energy functional and constraints can be discretized using Fourier pseudospectral schemes, thereby transforming the problem into an optimization task on a manifold. We derive vector transports by differentiating three existing retractions and propose an initial step size selection strategy based on the second-order approximation of the energy function for the proposed Riemannian optimization algorithm. In addition, a preconditioner is derived and used. To further accelerate the convergence, we combine the proposed algorithm with a multigrid method. Numerical experiments demonstrate the efficiency and accuracy of the proposed method while confirming the usefulness of our preconditioning technique and the effectiveness of the proposed strategy for initial step size selection.
Key words
spin-1 Bose-Einstein condensate, ground state, Riemannian conjugate gradient method, preconditioner
Status
Submitted