移动最小二乘近似函数中样条权函数的研究

局部边界积分方程方法是无网格方法的一种，它采用移动最小二乘近似试函数，且只包含中心在所考虑节点的局部边界上的边界积分．本文详细研究了移动最小二乘法中样条权函数的构造及其性质，并将各种样条权函数应用于弹性力学平面问题的局部边界积分方程方法中，研究了它对计算结果的收敛性、稳定性和精度的影响．算例表明，高阶样条权函数在局部边界积分方程方法中有好的收敛性、稳定性和精度．

A Study on the Spline Weight Function in the Moving Least Square Approximation

The local boundary integral equation method is one of the meshless methods. It uses the moving least square approximations and involves only boundary integration over a local boundary centered at the node in question. This paper studied the construction and properties of the spline weight function in the moving least square approximation. All kinds of spline weight functions were applied to solve the plane problems in the theory of elasticity by using the local boundary integral equation method, and their effects on the convergence, stability and accuracy of numerical results were also investigated. The numerical results show that higher spline weight functions in the local boundary integral equation method have excellent properties.