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

摘要

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 RxH(0)(1)(Omega) 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.