基于平均值插值求解势问题的宏单元法

MACRO-ELEMENT APPROACH BASED ON MEAN VALUE INTERPOLATION FOR SOLVING POTENTIAL PROBLEMS

在有限元法中采用宏单元(大单元)可以减少单元数量,进而降低网格生成的工作量,提高计算效率.本文利用多边形上的平均值插值构造宏单元的形函数,采用标准的Galerkin法推导出求解二维势问题的宏单元法.给出了宏单元形函数偏导数计算的方法.运用提出的宏单元法,分别采用多边形宏单元和含有任意数量边节点的宏单元,对一些二维势问题进行了分析计算.数值算例表明,本文提出的宏单元法具有较好的计算精度.

Using macro-element（large element）in finite element method,both the number of nodes and total number of degrees of freedom are reduced largely.So the meshes generation workload is decreased and the computational efficiency is increased. In this paper the shape functions of macro-element is constructed using mean value interpolation of polygon.Applying the well-known Galerkin procedure,the macro-element approach is derivative for 2D potential problems.The computational method of partial derivatives of shape functions for macro-elements is given.The shape functions constructed by mean value interpolation are neither polynomial forms nor rational functions forms. Applying the proposed macro-element approach,some 2D potential problems are analysis and computation by using polygonal macro-element or including arbitrary number side-nodes macro-element. Numerical results sustain the proposed method,which is successfully compared with exact analytical solutions.