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 $$\lambda $$ λ and eigenvector u separately, we regard the eigenpair $$(\lambda , u)$$ ( λ , u ) as one element in the composite space $${\mathbb {R}} \times H_0^1(\varOmega )$$ R × H 0 1 ( Ω ) 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.

中文翻译：

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基于牛顿迭代的玻色-爱因斯坦凝聚基态解的多重网格方法

本文提出了一种基于牛顿迭代法的玻色-爱因斯坦凝聚基态解的新型多重网格方法。我们没有将特征值 $$\lambda $$ λ 和特征向量 u 分开处理，而是将特征对 $$(\lambda , u)$$ ( λ , u ) 视为复合空间 $${\mathbb {R} 中的一个元素} \times H_0^1(\varOmega )$$ R × H 0 1 ( Ω ) 然后对非线性问题采用牛顿迭代步骤。因此在这种多重网格方案中，主要计算是在每个细化空间中求解线性离散边值问题，这可以提高玻色-爱因斯坦凝聚模拟的整体效率。