A multigrid method for the ground state solution of Bose–Einstein condensates based on Newton iteration

In this paper, a new kind of multigrid method is proposed for the ground state solution of Bose–Einstein condensates based on Newton iteration scheme. Instead of treating eigenvalue λ and eigenvector u separately, we regard the eigenpair ( λ , u ) as one element in the composite space R × H 0 1 ( Ω...

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Bibliographic Details
Published inBIT Vol. 61; no. 2; pp. 645 - 663
Main Authors Xu, Fei, Xie, Hehu, Xie, Manting, Yue, Meiling
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.06.2021
Springer Nature B.V
Subjects
Bose-Einstein condensates
Boundary value problems
Computational Mathematics and Numerical Analysis
Eigenvalues
Eigenvectors
Ground state
Iterative methods
Mathematics
Mathematics and Statistics
Numeric Computing
Finite element method
65N25
BEC
65B99
Multigrid method
65L15
GPE
Nonlinear eigenvalue problem
65N30
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Summary:In this paper, a new kind of multigrid method is proposed for the ground state solution of Bose–Einstein condensates based on Newton iteration scheme. Instead of treating eigenvalue λ and eigenvector u separately, we regard the eigenpair ( λ , u ) as one element in the composite space R × H 0 1 ( Ω ) and then Newton iteration step is adopted for the nonlinear problem. Thus in this multigrid scheme, the main computation is to solve a linear discrete boundary value problem in every refined space, which can improve the overall efficiency for the simulation of Bose–Einstein condensations.
ISSN:0006-3835
1572-9125
DOI:10.1007/s10543-020-00830-3