多重网格法求解三维静电场分布

本文将一种高效率的数值计算方法——多重网格法引入三维静电场分布的计算,多重网格法利用限制和延拓可迅速求得满足精度要求的场分布.研究了求解各种静电透镜电子光学系统三维场分布的多重网格法程序,验算了静电同心球模型的三维场分布.通过与目前在场计算中常用的有限差分法进行比较,可以看出多重网格法的计算效率和计算精度优于有限差分法.本文表明利用多重网格法计算三维场大大提高了场分布的计算效率,缩短了计算时间,因此为后续计算打下了良好的基础.

Multi-Grid Method Applied to Solve Three Dimensional Electrostatic Field Distribution

A highly efficient numerical algorithm by using Multi grid Method (MGM) is introduced to solve the three dimensional field distribution in the present paper.Formulae of the restriction and prolongation in MGM computation is deduced,and a 3D program of MGM is accomplished,which can solve the field distributions in electron optical systems for various electrostatic lenses.The 3D field distribution in an electrostatic concentric spherical model is tested with MGM algorithm and an algorithm based on Finite Difference Method (FDM) respectively.Comparing these two results in view of computational efficiency and computational accuracy,it appears that MGM is superior to FDM in solving electrostatic field distribution for the electron optics problem.This paper shows that the 3D field computation using MGM greatly improves the computational efficiency of field distributions in electron optical systems and shortens the computational time.