改进的移动最小二乘插值法研究

Researches on the Improved Interpolating Moving Least-squares Method

本文首先从内积的角度给出了移动最小二乘逼近法的新的推导方法,然后对Lancaster等提出的移动最小二乘插值法进行了重新推导,取在插值节点奇异的权函数,并对基函数进行部分正交化,建立了改进的移动最小二乘插值法,并证明了其形函数的插值性质。本文提出的改进移动最小二乘插值法的公式比Lancaster的公式更为简单,并可提高形函数的计算效率。本文为工程问题的插值型无网格方法提供了建立形函数的基本方法。

In this paper,based on the concept of an inner product,we propose a new method to obtain the moving least-squares approximation.The interpolating moving least-squares method proposed by Lancaster is thus improved.By taking a singular weight function in the interpolating points and orthogonalizing some of basis functions,an improved interpolating moving least-squares method is formulated and the property of the corresponding shape function is proved.The new method has a simpler formula and higher computing effciency compared with the Lancaster’s method.The proposed method can be used to form the shape function of the meshless method for engineering problems.