On solving three-dimensional electrostatic field distribution by multigridmethod

A highly efficient numerical algorithm using the multigrid method (MGM) is introduced to solve a three-dimensional (3-D) field distribution. Taking ad vantage of the restriction and prolongation: in MGM computation, a more acc urate field distribution can be acquired rapidly. According to the MGM algo rithm, a 3-D program is accomplished, which can solve the field distributio ns in electron optical systems for various electrostatic leases. The 3-D fi eld distribution in an electrostatic concentric spherical model is tested w ith the MGM algorithm and with an algorithm based on the finite difference method (FDM). Comparing these two results in terms of computational efficie ncy and computational accuracy, it appears that MGM is superior to FDM, whi ch is now used the most in field computations. This paper shows that the 3- D field computation using MGM greatly improves the computational efficiency of field distributions in electron optical systems and shortens the comput ational time.