基于核重构思想的配点型无网格方法的研究--一维问题

无网格方法按其离散原理可分为Galerkin型、配点型等。其中Galerkin型无网格方法的实施需要背景网格，不属于真正的无网格法；配点型无网格方法的实施不需要背景网格，是真正的无网格法。本文首先介绍了重构核点法的基本原理，然后基于核重构思想，与配点法相结合，以一维问题为例，研究了配点型无网格方法，对该方法构造过程中的近似函数及其导数的计算、修正函数的计算及方法的实现等问题进行了探讨。并结合若干典型算例，检验了其计算精度与收敛姓。

Study on point collocated meshless method based on reproducing kernel ideas for one-dimensional problems

Meshless method can be mainly divided into, according its discretizing principle, two kinds of type: Galerkin-type and point collocated-type. The implementation of Galerkin meshless method needs a background mesh. So it is not a true meshless method. While the point collocated meshless method is a real meshless method because its implementation does not need any background mesh. The basic principle of reproducing kernel particle method was first introduced in this paper. Then a new point collocated meshless method for one-dimensional problem was presented based on the reproducing kernel ideas combined with the point collocation method. The calculation of the approximation function and its derivatives, that of the correction function and its implementation were investigated. Numevical examples are given to show the accuracy and convergence of the proposed method.