无网格数值方法中的形函数研究

无网格法是近几年来发展的一种新的基于变分原理的数值计算方法,根据形函数构建和方程离散化方法的不同,分为不同的无网格法。文章主要讨论了移动最小二乘形函数的构建方法、性质。通过对曲线和曲面拟合算例的研究表明:权函数的选择、节点数目、影响域大小、基函数的选取等对形函数的精度和稳定性都有影响,通过数值实验给出了各参数的参考值。

Meshless numerical methods in the study of shape function

As a newnumerical computational method based on the principle of viriation,meshfree method has maintained a rapid development in recently years.With the different method of constructing the shape functions and discretized schemes of partial differential equations(PDES),we can obtain different meshfree method.In this paper,the basic principle of moving least squares approximation methods was introduced,the construction method for the shape functions were presented and the characteristic of shape functions we...