无网格方法中含参数指数权函数的研究

Research of an Exponential Function Used in Meshfree Method

选择合适的权函数及相应的影响半径是无网格方法中很重要的问题,在引入数值紧支域概念的基础上分析了含参数的指数权函数中参数的选取范围,综合考虑计算效率和精度后给出了参数的选取原则,并讨论了在特定的参数下的最优半径以及不同参数对最优半径的影响。

In meshfree methods it is an important problem how to select suitable weight function and corresponding optimal radius. Based on the notation, numerical support domain of a function posed in this paper,the proper range of the parameter appeared in a kind of weight function of exponential type is given. Furthermore, a guide on the selection about the parameter is suggested to meet the requirement of both accuracy and efficiency. For a given parameter the optimal radius of the support is obtained by a series of numerical tests. Finally, the effect of different parameters on the optimal radius is pointed out.