In this study, we present a new type of domain decomposition algorithm to obtain the ground state solution for Bose–Einstein condensates. Using our proposed algorithm, instead of directly solving the nonlinear eigenvalue problem, one only needs to solve a series of linear boundary value problems on a finite element space sequence using the domain decomposition method, and subsequently solve a small-scale nonlinear eigenvalue problem on an enriched space simultaneously. Because solving large-scale nonlinear eigenvalue problem directly is time intensive, our algorithm can obviously improve the efficiency of producing simulation for Bose–Einstein condensates. In addition, any domain decomposition algorithm for linear boundary value problems can be applied to our algorithm framework, which makes the algorithm considerably flexible. Two numerical experiments are presented in the paper to demonstrate the efficiency and scalability of our proposed algorithm.

在这项研究中，我们提出了一种新型的区域分解算法，以获取Bose-Einstein凝聚物的基态解。使用我们提出的算法，而不是直接解决非线性特征值问题，只需使用域分解方法解决有限元空间序列上的一系列线性边界值问题，然后解决一个小尺度非线性特征值问题。同时丰富空间。由于直接解决大规模非线性特征值问题是费时的，因此我们的算法可以明显提高Bose-Einstein凝聚物的模拟生成效率。此外，任何用于线性边值问题的域分解算法都可以应用于我们的算法框架，这使得该算法具有相当大的灵活性。