用自动网格剖分法求解二阶椭圆型偏微分方程

On the Computational Aspects of Auto Grid Splitting for Solving Second Order Elliptic Equations

从寻找一组合适的迭代初值出发 ,提出自动网格剖分方法。该方法可与其他各种方法相结合。以求解拉普拉斯方程第一类边值问题为例 ,重点讨论了自动网格剖分法与高斯迭代法和超松驰高斯迭代法相结合在求解二阶椭圆偏微分方程中的应用 ,实例证明 :采用自动网格剖分法后 ,收敛速度大大加快 ,并且随着网格的加密而愈发明显。因此 ,这是一种高效率的方法。

Based on the thought to find appropriate iterated initial values, an auto grid splitting (AGS) is presented This method can be combined with various methods for finite difference equation The combination of AGS with GS or SORGS is investigated to solve second order elliptic partial differential equations with the first boundary problems of the Laplace equation The results of examples show that computing time required is much less when AGS is applied and the effect is more obvious when grid more dense