湖南工业大学学报2025，Vol.39Issue(5)：98-102,5.DOI:10.3969/j.issn.1673-9833.2025.05.014
二维线性薛定谔方程的一种高效数值解法
An Efficient Numerical Solution for the Two-Dimensional Linear Schrödinger Equation
摘要
Abstract
In view of a solution of the two-dimensional linear Schrödinger equation,a new semi-discrete finite element two-grid algorithm has thus been constructed.The finite element solution of the Schrödinger equation originally solved on a fine grid is simplified to first solve the finite element solution of the original equation on a coarse grid,followed by the adoption of the numerical solution obtained on the coarse grid to decouple the real and imaginary parts of the equation on the fine grid,thus solving the finite element solutions of two elliptical equations.An analysis has been made of the error between the finite element solution of two grids and the exact solution under the H1 norm,with numerical experiments conducted.The numerical results show that the error order remains the same as that in reference[10],with the error smaller at different times.关键词
两网格算法/薛定谔方程/有限元方法Key words
two-grid algorithm/Schrödinger equation/finite element method分类
数学引用本文复制引用
王建云,钟子新,田智鲲..二维线性薛定谔方程的一种高效数值解法[J].湖南工业大学学报,2025,39(5):98-102,5.基金项目
湖南省普通高校教学改革基金资助项目(HNJG-2022-0834,HNJG-2023-0951) （HNJG-2022-0834,HNJG-2023-0951）
湖南省普通高校教学改革基金资助项目(HNJG-20230951) （HNJG-20230951）
湖南省教育厅科学研究基金资助重点项目(20240518,21A0361) （20240518,21A0361）
