定常线性薛定谔方程的一种高精度数值解法  

A High-Precision Numerical Solution Method for the Linear Steady Schrödinger Equation

作　　者：张红梅[1] 尹江华 ZHANG Hongmei;YIN Jianghua(College of Science,Hunan University of Technology,Zhuzhou Hunan 412007,China;Zhuzhou OKE Precision Cutting Tools Co.,Ltd.,Zhuzhou Hunan 412008,China)

机构地区：[1]湖南工业大学理学院,湖南株洲412007 [2]株洲欧科亿数控精密刀具股份有限公司,湖南株洲412008

出　　处：《湖南工业大学学报》2023年第6期69-73,102,共6页Journal of Hunan University of Technology

基　　金：湖南省自然科学省市联合基金资助项目(2021JJ50055);湖南工业大学教学改革研究基金资助项目(2022YB19);湖南省教育厅科学研究基金资助重点项目(23A0443);湖南省教育改革基金资助项目(HNJG-20230754)。

摘　　要：针对定常线性薛定谔方程构建了一种高效、快速的数值解法——两网格有限体积元算法。将求解区域剖分成了粗、细两种网格,先在粗网格上求原问题的有限体积元解,再在细网格上求一个解耦问题的解。算例验证了该方法极大地提高了求解效率,理论上也证明了该解与原问题的有限体积元解有相同的收敛阶。An highly efficient and fast numerical solution,i.e.two-gridfinite volume element method,has been constructed for the solution of the steady linear Schrödinger equation.With the solution domain divided into coarse andfine grids,an initial acquisition of thefinite volume element solution of the original problem can be achieved on the coarse grid,followed by the solution of a decoupling problem on the fine grid.The numerical example verifies the improved solving efficiency in the proposed scheme.It has also been theoretically proven that the solution is characterzied with the same convergence order as thefinite volume element solution of the original problem.

关 键 词：薛定谔方程 有限体积元算法 高精度 数值解法 

分 类 号：O241.8[理学—计算数学]