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

2021 ◽  
Author(s):  
Fei Xu ◽  
Hehu Xie ◽  
Manting Xie ◽  
Meiling Yue
Keyword(s):  
Ground State ◽  
Multigrid Method ◽  
Ground State Solution ◽  
Newton Iteration ◽  
State Solution ◽  
Bose Einstein

scholarly journals A Multigrid Method for Ground State Solution of Bose-Einstein Condensates

2016 ◽  
Vol 19 (3) ◽  
pp. 648-662 ◽  
Author(s):  
Hehu Xie ◽  
Manting Xie
Keyword(s):  
Finite Element ◽  
Boundary Value Problems ◽  
Ground State ◽  
Multigrid Method ◽  
Eigenvalue Problems ◽  
Boundary Value ◽  
Ground State Solution ◽  
State Solution ◽  
Linear Boundary ◽  
Bose Einstein

AbstractA multigrid method is proposed to compute the ground state solution of Bose-Einstein condensations by the finite element method based on the multilevel correction for eigenvalue problems and the multigrid method for linear boundary value problems. In this scheme, obtaining the optimal approximation for the ground state solution of Bose-Einstein condensates includes a sequence of solutions of the linear boundary value problems by the multigrid method on the multilevel meshes and some solutions of nonlinear eigenvalue problems some very low dimensional finite element space. The total computational work of this scheme can reach almost the same optimal order as solving the corresponding linear boundary value problem. Therefore, this type of multigrid scheme can improve the overall efficiency for the simulation of Bose-Einstein condensations. Some numerical experiments are provided to validate the efficiency of the proposed method.

Pseudo-Arclength Continuation Algorithms for Binary Rydberg-Dressed Bose-Einstein Condensates

2016 ◽  
Vol 19 (4) ◽  
pp. 1067-1093 ◽  
Author(s):  
Sirilak Sriburadet ◽  
Y.-S. Wang ◽  
C.-S. Chien ◽  
Y. Shih
Keyword(s):  
Ground State ◽  
Nonlinear Term ◽  
Ground State Solution ◽  
State Solution ◽  
Divide And Conquer ◽  
Continuation Methods ◽  
Solution Curve ◽  
Bose Einstein ◽  
Curve Tracing ◽  
Nonlocal Nonlinear

AbstractWe study pseudo-arclength continuation methods for both Rydberg-dressed Bose-Einstein condensates (BEC), and binary Rydberg-dressed BEC which are governed by the Gross-Pitaevskii equations (GPEs). A divide-and-conquer technique is proposed for rescaling the range/ranges of nonlocal nonlinear term/terms, which gives enough information for choosing a proper stepsize. This guarantees that the solution curve we wish to trace can be precisely approximated. In addition, the ground state solution would successfully evolve from one peak to vortices when the affect of the rotating term is imposed. Moreover, parameter variables with different number of components are exploited in curve-tracing. The proposed methods have the advantage of tracing the ground state solution curve once to compute the contours for various values of the coefficients of the nonlocal nonlinear term/terms. Our numerical results are consistent with those published in the literatures.

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