Solving unsteady Schr?dinger equation using the improved element-free Galerkin method  

作　　者：程荣军 程玉民 

机构地区：[1]Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211, China [2]Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

出　　处：《Chinese Physics B》2016年第2期35-43,共9页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Grant No.11171208);the Natural Science Foundation of Zhejiang Province,China(Grant No.LY15A020007);the Natural Science Foundation of Ningbo City(Grant No.2014A610028);the K.C.Wong Magna Fund in Ningbo University,China

摘　　要：By employing the improved moving least-square （IMLS） approximation, the improved element-free Galerkin （IEFG） method is presented for the unsteady Schrodinger equation. In the IEFG method, the two-dimensional （2D） trial function is approximated by the IMLS approximation, the variation method is used to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. Because the number of coefficients in the IMLS approximation is less than in the moving least-square （MLS） approximation, fewer nodes are needed in the entire domain when the IMLS approximation is used than when the MLS approximation is adopted. Then the IEFG method has high computational efficiency and accuracy. Several numerical examples are given to verify the accuracy and efficiency of the IEFG method in this paper.By employing the improved moving least-square （IMLS） approximation, the improved element-free Galerkin （IEFG） method is presented for the unsteady Schrodinger equation. In the IEFG method, the two-dimensional （2D） trial function is approximated by the IMLS approximation, the variation method is used to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. Because the number of coefficients in the IMLS approximation is less than in the moving least-square （MLS） approximation, fewer nodes are needed in the entire domain when the IMLS approximation is used than when the MLS approximation is adopted. Then the IEFG method has high computational efficiency and accuracy. Several numerical examples are given to verify the accuracy and efficiency of the IEFG method in this paper.

关 键 词：meshless method improved moving least-square （IMLS） approximation improved element-freeGalerkin （IEFG） method Schr6dinger equation 

分 类 号：O241.8[理学—计算数学]