岩体力学边界元数值计算中插值函数的改进

Improvement of interpolation function in mechanics boundary element numerical calculation

在样条函数替代边界元数值计算中,常用分段多项式插值作函数逼近,其优点非常突出:一方面,在给定区间上用三次样条逼近任意有二阶连续导数的函数,均方差最小;另一方面,三次样条的阶次较低,结点值的误差不会因插值计算而扩散很远,插值计算的稳定性好。文中分析样条插值函数特征,给出了具体求解格式。数值计算中引入样条函数,使最终系数矩阵变成带宽很窄的条带阵,为解决边界元数值计算中遇到的困难奠定了基础。

The spline function substitutes for the stepwise polynomial interpolation method which is commonly used in the boundary element numerical calculation and makes functional approximation, its advantage is very outstanding： First, using the cubic spline function to approach any function which has second-order continuous derivative in a given inter-zone can gain a minimal mean square deviation, Second, because the orders of the cubic spline function is lower, the error of nodal value won＇t deviate too much, The stability of the interpolation calculation is good. Taking the homogeneous boundary element as an example, by reforming spline interpolation, the whole quotient matrix was turned into a strip one with a very narrow strip width, It lays the foundation for solving the boundary element problems.