Year: 2019
Author: Ning Zhang, Fei Xu, Hehu Xie
International Journal of Numerical Analysis and Modeling, Vol. 16 (2019), Iss. 5 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2019-IJNAM-13254
International Journal of Numerical Analysis and Modeling, Vol. 16 (2019), Iss. 5 : pp. 789–803
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: BEC GPE nonlinear eigenvalue problem multigrid tensor finite element method asymptotically optimal efficiency.