  In this paper, a new kind of multigrid method is proposed for the ground
state solution of Bose-Einstein condensates based on Newton iteration method.
Instead of treating eigenvalue $\lambda$ and eigenvector $u$ respectively, we
regard the eigenpair $(\lambda, u)$ as one element in the composite space $\R
\times H_0^1(\Omega)$ and then Newton iteration method is adopted for the
nonlinear problem. Thus in this multigrid scheme, we only need 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.
