一种新的数值方法——无网格伽辽金法(EFGM)  

A new numerical method element free Galerkin method (EFGM)

作　　者：庞作会[1] 葛修润[1] 郑宏[1] 王水林[1] 

机构地区：[1]中国科学院武汉岩土力学研究所

出　　处：《计算力学学报》1999年第3期320-329,共10页Chinese Journal of Computational Mechanics

摘　　要：无网格伽辽金法（ＥＦＧＭ）是近几年发展起来的与有限元相似的一种数值算法。它采用移动的最小二乘法构造形函数，从能量泛函的弱变分形式中得到控制方程，并用拉氏乘子满足本征边界条件，从而得到偏微分方程的数值解。该法只需节点信息，不需将节点连成单元；此外，还有精度高、后处理方便等优点。本文介绍其基本原理及实现过程，并用算例表明，该法具有一定的发展前景。Element free Galerkin method (EFGM), similar to FEM, is a new numerical method developed recently. In EFGM, in order to get a numerical solution for a partial differential equation, shape function is constructed by Moving Least Square (MLS), control equation is produced from the weak form of variational equation and Lagrange multipliers are used to satisfy essential boundary conditions. The merits of EFGM are: (1) only nodal data are necessary, i. e. there is no need to join nodes into elements; (2) high accuracy can be achieved; (3) postprocess is easy, etc. In this paper, the basic principle of EFGM and the implementation of it are introduced, in addition, several examples are given to show that this method is promising.

关 键 词：无网格 权函数 拉氏乘子 伽辽金法 EFGM 

分 类 号：O241.8[理学—计算数学]