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A Multigrid Method for Ground State Solution of Bose-Einstein Condensates

Part of: Numerical analysis: Ordinary differential equations Acceleration of convergence Partial differential equations, boundary value problems

Published online by Cambridge University Press:  16 March 2016

Hehu Xie  and
Manting Xie
Hehu Xie*
Affiliation:
LSEC, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Manting Xie
Affiliation:
LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
*
*Corresponding author. Email addresses:hhxie@lsec.cc.ac.cn (H. Xie), xiemanting@lsec.cc.ac.cn (M. Xie)

Abstract

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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.

Keywords

BECGPEeigenvalue problemmultigridmultilevel correctionfinite element method

MSC classification

Secondary: 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 65N25: Eigenvalue problems 65L15: Eigenvalue problems 65B99: None of the above, but in this section

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 3 , March 2016 , pp. 648 - 662
Copyright
Copyright © Global-Science Press 2016 

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