无网格法计算误差分析

Error analysis with the meshless method

探讨了无网格法中形函数的性态及对计算结果的影响 ,讨论了无网格法产生误差的原因 .主要分析了无网格伽辽金法 (EFGM )节点不良分布以及采用一般高次多项式基构造形函数时 ,致使形函数中矩阵A(X)病态 ,从而导致全局数值解振荡的原因 .就不同的基函数对插值函数及无网格法的计算精度的影响作了分析比较 ,得出了基函数的选取标准 ,算例说明使用三次基函数计算精度最高 .

The properties and characteristics of the shape functions in meshless method and their influence on the numerical results were dealt with. The reasons why the error appeared in this method were discussed. It was showed that the shape matrix A ( X ) was ill conditioned when Element Free Galerkin method (EFGM) used high order polynomial basis and the nodes were ill distributed. The influence of different basic functions on the interpolation functions and the computed accuracy were analyzed and compared. Based on the above analysis, the criterion for choosing the basis function was obtained. The numerical examples were given to show that the highest accuracy can be achieved by using cubic basis function.