耦合径向基函数与多项式基函数的无网格方法

A Meshless Method Based on Coupled Radial and Polynomial Basis Functions

耦合径向基函数和多项式基函数,形成一种新的近似函数.该近似函数对散乱分布的离散数据点进行逼近时,只需节点信息,不需要划分网格.详细描述了耦合近似函数的建立、属性、插值行为及其形函数和形函数导数的性质.最后引入修正变分原理和单位分解积分技术求解边值问题,并给出了计算实例,表明耦合径向基函数和多项式基函数是一种非常有效的方法.

A new approximate method based on coupled radial basis functions and polynomial basis functions is presented.Only nodes information is needed when this method is used for interpolation over a set of discrete nodes,the background mesh is totally unnecessary.The establishment,properties,interpolation behaviors of approximate functions,the shape functions and their derivatives are described in detail.The modified variation principle and partition of unity quadrature are employed with coupled approximate function to solve boundary value problems. Numerical examples show excellent agreement with exact solutions.