紧支试函数加权残值法

将紧支函数引入加权残值法中，提出了紧支试函数加权残值法，其数值格式具有和有限元相似的窄带系数矩阵，提高了加权残值法的计算效率．在紧支试函数加权残值的基础上，导出了紧支试函数直接配点法、紧支试函数Hermite配点法和紧支试函数最小二乘配点法的具体格式，并且对几个典型算例进行了分析．与配点法相比，这些方法精度高，稳定性好，而与Galerkin法相比，这些方法效率高．

WEIGHTED RESIDUAL METHOD WITH COMPACTLY SUPPORTED TRIAL FUNCTIONS

The Weighted Residual Method (WRM) is an effective method for solving Partial Differential Equations (PDEs). However, the trial functions used in WRM are usually globally supported so that the resultant stiffness matrix is a full matrix and significant computational effort is required. In this paper, WRM with compactly supported trial functions is developed, which may result in a banded sparse coefficient matrix so that the computational effort is reduced. WRM with compactly supported trial functions can be taken as the theoretical basis to summarize and investigate meshless methods systematically, from which all existing meshless methods can be obtained and new meshless methods can also be derived. As an example, the Direct Collocation, Hermite Collocation and Least-squares Collocation with compactly supported trial functions are established, whose coefficient matrices are banded and sparse so that the computational effort required is reduced significantly. Furthermore, the methods established are truly mesh-free and very efficient. Numerical examples, including a cantilever beam and an infinite plate with a central circular hole, are presented to illustrate the performance of the proposed methods.