三分谢尔宾斯基垫片上的调和函数与双调和函数的算法

Algorithms for Harmonic Functions and Bi-harmonic Function on the level-3 Sierpinski Gasket

在这篇文章中,我们首先介绍了三分谢尔宾斯基垫片和标准拉普拉斯算子;其次,我们推导出了三分谢尔宾斯基垫片上调和函数与双调和函数的算法。图的顶点上这些函数的算法最后得出了预垫片,也就是近似三分谢尔宾斯基垫片。

In this paper, first, we introduce the level -3 Sierpinski Gasket and standard Laplacians on it;sec- ond,we describe algorithms for the exact computation of harmonic function, bi - harmonic function for the standard Laplacians on the level -3 Sierpinski Gasket （SG3 ）. These algorithms allow for the computation of the values of these functions on the vertices of the graphs, the pre - gaskets Gm, that is approximate SG3.