Poisson方程差分格式的SOR方法中最优松弛因子的回归分析方法

The Regression Method for Determining the Optimal Relaxation Parameter of SOR Method in Finite Difference Discretization to Poisson's Equations

针对二维Poisson方程各种边值问题的典型差分格式,使用回归分析方法给出了求解这些格式的SOR方法中最优松弛因子的计算公式。统计分析与实际计算表明这些公式具有非常好的计算效果。

It is difficult to determine the optimal relaxation parameter for the SOR iteration method. This paper presents some empirical formulae for optimal relaxation parameters by regression analysis method for the linear systems derived from finite difference discretization to Poisson's equations. Both statistical tests and practical computations show these formulae have very high computational efficiency.