任意网格差分方程的新解法

A New Method for Solving Finite Difference Equations on Arbitrary Irregular Grids

任意网格差分法适用于结构分析的各个领域,但由任意网格构造的差分方程缺乏对称、正定、对角占优等优良性质。故至今尚未见到求解这种差分方程的有效方法。本文采用稀疏技术消去法求解这类方程,极大地节省了计算机时,所得结果的计算精度令人满意。文中讨论了稀疏技术消去法的各种策略,给出了计算弹性力学问题的几个实例。

Finite difference method on arbitrary irregular grids is widely used in all fields of structural analysis.However,the effective solution of its equations is a problem yet to be solved since they are not symmetric, diagonal element dominative and positive definite.In this paper,the elimination method by use of sparse matrix techniques is applied to solve this kind of FD equations.The precisions of the results are satisfactory while computing time is greatly saved.Several tactics of elimination method by use of sparse matrix techniques are discussed,and their efficiency is illustrated by three numerical solutions in structural analysis.