用于旋转情况下 stationary Gross-Pitaevskii 方程的有限元工具箱
A finite-element toolbox for the stationary Gross-Pitaevskii equation with rotation
AI总结：
本文提出基于经典有限元方法的数值工具箱，用于计算 stationary Gross-Pitaevskii 方程的解，包含优化算法和自适应网格技术，适用于二维和三维 Bose-Einstein 凝聚体旋转模拟。
摘要：
我们提出了一种新的数值系统，使用经典有限元方法和网格自适应性来计算 stationary Gross-Pitaevskii 方程的稳态解。该程序作为 FreeFem++ 的工具箱编写，适用于所有现有操作系统。该方法隐藏了有限元实现的全部技术问题，使各种数值算法易于实现。两种稳健且优化的数值方法被实现以最小化 Gross-Pitaevskii 能量：基于 Sobolev 梯度的最陡下降法和基于最新优化库 Ipopt 的最小化算法。对于这两种方法，实现了网格自适应策略以减少计算时间并提高存在涡旋时的局部空间精度。提供了不同运行案例用于旋转 Bose-Einstein 凝聚体的 2D 和 3D 配置。还提供了一个可选的图形用户界面，允许轻松运行预定义案例或使用用户定义的参数文件。我们还提供了多种后处理工具（如涡旋识别），有助于从模拟中提取物理特征。该工具箱非常灵活，可以轻松适应不同的物理模型。
英文摘要：
We present a new numerical system using classical finite elements with mesh adaptivity for computing stationary solutions of the Gross-Pitaevskii equation. The programs are written as a toolbox for FreeFem++ (www.freefem.org), a free finite-element software available for all existing operating systems. This offers the advantage to hide all technical issues related to the implementation of the finite element method, allowing to easily implement various numerical algorithms.Two robust and optimised numerical methods were implemented to minimize the Gross-Pitaevskii energy: a steepest descent method based on Sobolev gradients and a minimization algorithm based on the state-of-the-art optimization library Ipopt. For both methods, mesh adaptivity strategies are implemented to reduce the computational time and increase the local spatial accuracy when vortices are present. Different run cases are made available for 2D and 3D configurations of Bose-Einstein condensates in rotation. An optional graphical user interface is also provided, allowing to easily run predefined cases or with user-defined parameter files. We also provide several post-processing tools (like the identification of quantized vortices) that could help in extracting physical features from the simulations. The toolbox is extremely versatile and can be easily adapted to deal with different physical models.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
