Abstract
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 \(\lambda \) and eigenvector u separately, we regard the eigenpair \((\lambda , u)\) as one element in the composite space \({\mathbb {R}} \times H_0^1(\varOmega )\) 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.
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Communicated by Marko Huhtanen.
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This work was supported in part by the National Key Research and Development Program of China (2019YFA0709601), National Natural Science Foundations of China (NSFC 11771434, 11801021, 91730302, 91630201), the National Center for Mathematics and Interdisciplinary Science, CAS.
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Xu, F., Xie, H., Xie, M. et al. A multigrid method for the ground state solution of Bose–Einstein condensates based on Newton iteration. Bit Numer Math 61, 645–663 (2021). https://doi.org/10.1007/s10543-020-00830-3
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DOI: https://doi.org/10.1007/s10543-020-00830-3