A Multigrid Method for Ground State Solution of Bose-Einstein Condensates. (16th March 2016)

• Record Type: Journal Article
• Authors: Xie, Hehu; Xie, Manting
• Is Part Of: Communications in computational physics. Volume 19:Number 3(2016:Mar.)
• Page Start: 648
• Page End: 662
• Publication Date: 2016-03-16
• Subjects: 65N30, -- 65N25, -- 65L15, -- 65B99; BEC, -- GPE, -- eigenvalue problem, -- multigrid, -- multilevel correction, -- finite element method; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.191114.130715a
• Languages: English
• ISSNs: 1815-2406

Abstract

Abstract: A multigrid method is proposed to compute the ground state solution of Bose-Einstein condensations by the finite element method based on the multilevel correction for eigenvalue problems and the multigrid method for linear boundary value problems. In this scheme, obtaining the optimal approximation for the ground state solution of Bose-Einstein condensates includes a sequence of solutions of the linear boundary value problems by the multigrid method on the multilevel meshes and some solutions of nonlinear eigenvalue problems some very low dimensional finite element space. The total computational work of this scheme can reach almost the same optimal order as solving the corresponding linear boundary value problem. Therefore, this type of multigrid scheme can improve the overall efficiency for the simulation of Bose-Einstein condensations. Some numerical experiments are provided to validate the efficiency of the proposed method.