A novel adaptive finite element method for the ground state solution of Bose-Einstein condensates
作者：
Highlights：
• A novel adaptive finite element method is proposed for the ground state solution of Bose-Einstein Condensates. The new adaptive scheme only needs to solve a series of linear boundary value problems on the adaptive spaces and some low dimensional nonlinear eigenvalue problems on a correction space.
• The involved linear boundary value problems will be solved by classical adaptive multi- grid method.
• The overall efficiency of the new adaptive algorithm will be comparable to that of adaptive finite element method for linear boundary value problem.
• As the standard adaptive finite element method, we can also give the rigorous proof for the convergence and optimal complexity.
• The validity of the proposed methods are demonstrated from both theoretical and numerical aspects.
摘要
•A novel adaptive finite element method is proposed for the ground state solution of Bose-Einstein Condensates. The new adaptive scheme only needs to solve a series of linear boundary value problems on the adaptive spaces and some low dimensional nonlinear eigenvalue problems on a correction space.•The involved linear boundary value problems will be solved by classical adaptive multi- grid method.•The overall efficiency of the new adaptive algorithm will be comparable to that of adaptive finite element method for linear boundary value problem.•As the standard adaptive finite element method, we can also give the rigorous proof for the convergence and optimal complexity.•The validity of the proposed methods are demonstrated from both theoretical and numerical aspects.
论文关键词：Bose-Einstein condensates,Adaptive multigrid method,Multilevel correction method,Convergence,Optimal complexity
论文评审过程：Received 30 March 2020, Revised 18 May 2020, Accepted 24 May 2020, Available online 10 June 2020, Version of Record 10 June 2020.
论文官网地址：https://doi.org/10.1016/j.amc.2020.125404
