基于有限元自动生成系统(FEPG)的组合网格算法

A Composite Grid Method Based on the System of Finite Element Program Generator(FEPG)

针对工程计算中经常出现的局部特性(特别是奇性)问题,和以往解决此类问题的算法的局限性,提出一种基于有限元自动生成系统(FEPG)的组合网格算法.该算法采用两套网格求解,在整个求解区域采用较粗网格,不考虑奇异的影响;而在奇异附近区域采用较细的网格,考虑奇异的影响;整体粗网格求解和局部细网格求解反复迭代,求得最终结果.该算法用于实际工程计算的迭代次数少,与常用的有限元方法所求得的解相符合,为求解大型实际复杂问题提供了一个好的算法和思路.

We in this paper present a composite grid method based on the system of finite element program generator （denoted by FEPG） to solve finite element problems with local singularity, which often occurs in engineering and scientific computing. Composite grid method uses a coarse mesh for the whole area without considering the impact of singularity and a fine mesh for the local singular area considering the impact of singularity respectively. It solves the global coarse mesh problem and the local fine mesh problem iteratively and obtains the final result with very small computation. This method presents a good idea for solving complex problems.