自然邻点插值在渗流场/应力场构造中的应用

计算渗流场或初始地应力场的网格一般要比实际结构分析的网格大，因此结构分析时需要将大网格中的渗流场或初始地应力场转换到小的结构分析网格中。若有大网格信息，就可以利用有限元形函数进行转换。但有时只有大网格结点坐标和相应的物理量，此时一般采用加权平均法进行转换，这种转换的精度不是太高。自然邻点插值法是基于给定结点的Voronoi图，通过自然邻点的坐标值构造插值函数，因此特别适合只有结点坐标和相应的物理量，而要将其应用于另一种网格模型的情况。给出了两种自然邻点插值的构造方式及其具体实现步骤。算例表明采用自然邻点插值构造场的精度很高。

Natural Neighbor Interpolation and Its Application in Formation of Seepage Field / Initial Stress Field

As the computation mesh for seepage field or initial stress field is generally bigger than that for real structural analysis, it is necessary in the structural analysis to transform the seepage field or initial stress field from the big mesh into the small mesh. If the information of big mesh is known, the transformation can be done with the shape function of finite element method. But sometimes only the coordinate and its corresponding physical quantity are known, the transformation is then generally done by weighted averaging method, which has a not high accuracy of transformation. Natural neighbor interpolation method constructs the interpolation function with the coordinate values of natural neighbors based on Voronoi diagram, therefore, it especially suits the case where only the coordinate and its corresponding physical quantity are known and the quantity has to be applied to a mesh model of another type. The formation mode and the realization procedure by two natural neighbor interpolation methods are described and the real computation cases show that the natural neighbor interpolation method has a high accuracy in field formation.