Volume 16, Issue 5
An Efficient Multigrid Method for Ground State Solution of Bose-Einstein Condensates

Ning Zhang, Fei Xu & Hehu Xie

DOI:

Int. J. Numer. Anal. Mod., 16 (2019), pp. 789-803.

Published online: 2019-08

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  • Abstract

An efficient multigrid method is proposed to compute the ground state solution of Bose-Einstein condensations by the finite element method based on the combination of the multigrid method for nonlinear eigenvalue problem and an efficient implementation for the nonlinear iteration. The proposed numerical method not only has the optimal convergence rate, but also has the asymptotically optimal computational efficiency which is independent from the nonlinearity of the problem. The independence from the nonlinearity means that the asymptotic estimate of the computational work can reach almost the same as that of solving the corresponding linear boundary value problem by the multigrid method. Some numerical experiments are provided to validate the efficiency of the proposed method.

  • Keywords

BEC, GPE, nonlinear eigenvalue problem, multigrid, tensor, finite element method, asymptotically optimal efficiency.

  • AMS Subject Headings

65N30, 65N25, 65L15, 65B99

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

zhangning114@lsec.cc.ac.cn (Ning Zhang)

xufei@lsec.cc.ac.cn (Fei Xu)

hhxie@lsec.cc.ac.cn (Hehu Xie)

  • BibTex
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@Article{IJNAM-16-789, author = {Zhang , Ning and Xu , Fei and Xie , Hehu }, title = {An Efficient Multigrid Method for Ground State Solution of Bose-Einstein Condensates}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2019}, volume = {16}, number = {5}, pages = {789--803}, abstract = {

An efficient multigrid method is proposed to compute the ground state solution of Bose-Einstein condensations by the finite element method based on the combination of the multigrid method for nonlinear eigenvalue problem and an efficient implementation for the nonlinear iteration. The proposed numerical method not only has the optimal convergence rate, but also has the asymptotically optimal computational efficiency which is independent from the nonlinearity of the problem. The independence from the nonlinearity means that the asymptotic estimate of the computational work can reach almost the same as that of solving the corresponding linear boundary value problem by the multigrid method. Some numerical experiments are provided to validate the efficiency of the proposed method.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/13254.html} }
TY - JOUR T1 - An Efficient Multigrid Method for Ground State Solution of Bose-Einstein Condensates AU - Zhang , Ning AU - Xu , Fei AU - Xie , Hehu JO - International Journal of Numerical Analysis and Modeling VL - 5 SP - 789 EP - 803 PY - 2019 DA - 2019/08 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/13254.html KW - BEC, GPE, nonlinear eigenvalue problem, multigrid, tensor, finite element method, asymptotically optimal efficiency. AB -

An efficient multigrid method is proposed to compute the ground state solution of Bose-Einstein condensations by the finite element method based on the combination of the multigrid method for nonlinear eigenvalue problem and an efficient implementation for the nonlinear iteration. The proposed numerical method not only has the optimal convergence rate, but also has the asymptotically optimal computational efficiency which is independent from the nonlinearity of the problem. The independence from the nonlinearity means that the asymptotic estimate of the computational work can reach almost the same as that of solving the corresponding linear boundary value problem by the multigrid method. Some numerical experiments are provided to validate the efficiency of the proposed method.

Ning Zhang, Fei Xu & Hehu Xie. (2019). An Efficient Multigrid Method for Ground State Solution of Bose-Einstein Condensates. International Journal of Numerical Analysis and Modeling. 16 (5). 789-803. doi:
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