一个基于子结构法解椭圆型方程的预处理器  

A Precondition for Elliptic Problems Discretized by Nonconforming Finite Elements Via Substruring

作　　者：朱建伟[1] 

机构地区：[1]长江大学一年级工作部,湖北荆州434023

出　　处：《长江大学学报（自科版）（上旬）》2009年第01X期115-116,共2页JOURNAL OF YANGTZE UNIVERSITY (NATURAL SCIENCE EDITION) SCI ＆ ENG

基　　金：国家自然科学基金项目（70371023）.

摘　　要：基于子结构法，提出了一个求解二阶椭圆型方程的一个预处理器。考虑到非协调元的特点，区域内交叉点不是单元边的中点，构造的预处理器便于并行求逆，且可使系统的条件数降为O（（1＋lnH/h）max（1＋H^-2,1＋lnH/h））。由于预处理器与内节点无关，即无需解粗网格方程，因此是一个更为简单、有效的预处理器。Based on substructuring,a preconditioner is developed for second order elliptic problem discretized by nonconforming finite elements,They can be inversed in parallel easily and applied to preconditioning the stiff matrix with the condition number no more than O[[1+lnH/h]max[1+H-2,1+lnH/h],where H,h are respectively the coarse and the fine mesh parameters.What is more important is that all the presented preconditioner is irrevant to the internal crosspoints,so that it is unnecessary to solve the coarse mesh equation in the preconditioning process.

关 键 词：预处理器 区域分解算法 条件数 

分 类 号：O241[理学—计算数学]