A Multigrid Method for Ground State Solution of Bose-Einstein Condensates (Communications in Computational Physics, 2018)
A multigrid method is proposed to compute the ground state solution ofBose-Einstein condensations by the finite element method based on the multilevel correctionfor eigenvalue problems and the multigrid method for linear boundary valueproblems. In this scheme, obtaining the optimal approximation for the ground statesolution of Bose-Einstein condensates includes a sequence of solutions of the linearboundary value problems by the multigrid method on the multilevel meshes and somesolutions of nonlinear eigenvalue problems some very low dimensional finite elementspace. The total computational work of this scheme can reach almost the same optimalorder as solving the corresponding linear boundary value problem. Therefore,this type of multigrid scheme can improve the overall efficiency for the simulation ofBose-Einstein condensations. Some numerical experiments are provided to validatethe efficiency of the proposed method.