求解玻色-爱因斯坦基态解的一种SQP优化方法  

A SQP OPTIMIZATION METHOD FOR SOLVING BOSE-EINSTEIN GROUND STATE SOLUTION

作　　者：刘文杰 张雪琳 王汉权[1,3] Liu Wenjie;Zhang Xuelin;Wang Hanquan(School of Mathematics and Statistics,Yunnan University of Finance and Economics,Kunming 650221,China;School of Mathematics,Sichuan University,Chengdu 610064,China;School of Mathematics,Yunnan Normal University,kunming,Yunnan Province,650504)

机构地区：[1]云南财经大学统计与数学学院,昆明650221 [2]四川大学数学学院,成都610064 [3]云南师范大学数学学院,昆明650504

出　　处：《数值计算与计算机应用》2023年第3期237-251,共15页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金项目(11871418、11971120);云南基础研究计划重点项目(202101AS070044)资助。

摘　　要：近年来,有关玻色-爱因斯坦凝聚态基态解的实验研究已经取得了一系列重要的成果.本文在相关研究成果的基础上,首先通过降维和无量纲化方法将玻色-爱因斯坦凝聚态基态解问题转换成能量泛函极值问题,在离散该方程时,我们使用有限差分法和傅里叶谱方法分别离散该能量泛函方程的一维和二维情形.其次,本文采用了一种高效的数值优化算法-SQP优化方法来求解玻色-爱因斯坦凝聚态基态解问题并运用该算法分别对一维和二维的能量泛函极小值问题进行数值模拟.最后通过分析实验数据结果和图像,得出该算法能提高能量函数值的精确性.In recent years,a series of important achievements have been made in experimental research on ground state solutions of Bose-Einstein condensates.In this paper,on the basis of relevant research results,Firstly,the ground state solution problem of Bose-Einstein condensate is transformed into an energy functional extremum problem by means of reductive and dimensionless methods,In discretizing this equation,the finite difference method and Fourier spectral method are used to discretize the one and two-dimensional cases of the energy functional equation.The second,In this paper,SQP optimization method is an eficient numerical optimization algorithm used to solve the ground state solution of Bose-Einstein condensate and the algorithm is used to simulate one and two-dimensional energy functional minimum problems.Finally,by analyzing the experimental data and images,it is concluded that the algorithm can improve the accuracy of energy function value.

关 键 词：玻色-爱因斯坦 有限差分法 傅里叶谱方法 SQP优化方法 数值计算 

分 类 号：O469[理学—凝聚态物理]