基于节点计算的自适应数值积分及其程序实现

数值积分是基于节点计算的数值分析方法的关键技术之一。针对完全无网格法的计算要求，提出了一种能自动适应任意计算域上各种节点分布方式的数值积分算法。该算法能随计算点的位置不同，自动确定积分域及积分域内的求积点，计算出数值积分结果，给出了临空边坡滑移体和圆孔方板2个实例。结果表明，按文中算法编制的程序具有良好的边界再生能力和较高的计算精度，可作为基于节点数值分析方法的一个程序模块，用于实际计算。底层算法思想，使得程序可方便地转换为其他计算语言。

An adaptive numerical integration and its program based on nodes calculation

Numerical integration is one of the key techniques for numerical methods based on the nodes calculation.In order to meet the calculation requirements of the true meshless methods,an adaptive numerical integration algorithm for different integration domains associated with the position of the nodes is proposed.The method can be used to determine the integration region and its Gaussian integral points automatically.Two examples,i.e.a slope body which is up against vacancy and a square plate with a hole,are analyzed.The results show that the program based on the algorithms proposed have good boundary re-shape character and high accuracy.The program can be used as a general program module for the numerical methods and applied to practice.It is easily to interpret the program to other computer languages since its basic algorithms.