无网格方法是近年发展起来的一种新的数值计算方法，根据近似函数构建方法和微分方程离散方法的不同，可以构建出许多不同的无网格方法。该文简述了无网格方法的理论基础；介绍近似函数的构建方法和微分方程的离散方法，并以移动最小二乘近似方法为例，分析了权函数和形函数的特征。分析结果显示：径向基函数和点插值法均具有d 函数属性，但计算稳定性差；移动最小二乘近似函数不具有d 函数属性，但计算比较稳定；无网格方法中的3种离散方法不同之处在于：配点法不需要积分，计算量小，计算稳定性差；Galerkin方法需要借助背景网格进行积分，它不是真正的无网格方法；Petrov-Galerkin方法，是一种真正的无网格方法，它需要对每个子域进行积分，计算工作量较大。

Meshless method is a recently-developed new numerical approach. Many different meshless methods have been constructed based on different approximation function methods and different discretized schemes of partial differential equations (PDEs). In this paper, its basic principle was introduced and the construction methods for the approximation function and the discretization of the partial differential equations were presented. The characteristics of weight function and the shape function were analyzed in detail taking the moving least-squares (MLS) method as an example. Results show that radial basis function (RBF) and point interpolation methods possess Kronecker Delta function property (d function), but the robustness is poor in some cases; the MLS approximation function does not possess Kronecker Delta function property, but it has good robustness. Differences among the three discretization schemes of meshless method are as follows：the collocation method requires no numerical integration and very little computational time while its robustness is poor; Galerkin method is not a truly meshless method due to the background meshes required for integration; the Petrov-Galerkin method is a truly meshless method and need numerical integration in each sub-domain, so it needs more computational time.

国家自然科学基金项目(50636050)。