关于二阶椭圆方程区域分裂法的最优预处理  

ON OPTIMAL PRECONDITIONING IN THE DOMAIN DECOMPOSITION METHOD FOR SECOND ORDER ELLIPTIC EQUATION

作　　者：张胜[1] 

机构地区：[1]复旦大学数学研究所

出　　处：《计算数学》1993年第2期235-241,共7页Mathematica Numerica Sinica

摘　　要：§0.引言 区域分裂是与微分方程数值解的并行计算的数学基础密切相关的,预处理共轭梯度法是区域分裂的一个主要途径,寻找好的预处理子是关键问题,本文给出一个较一般性的方法,预处理过程包括一个整体小规模问题和若干个独立的局部子问题,整体问题和局部问题的选取均有极大的任意性。In this paper, a general theory for the construction of preconditioners is given, the processof preconditioning is composed of the resolution of a small scale global problem and a numberof independent local subproblems. The global and local subproblems can be selected arbitra-rily. The condition number of the preconditioned system is estimated by some characteristicnumbers related to global and local subproblems. With a proper selection of global and localsubproblems, the optimal preconditioner can be obtained, and the condition number is independentof the scale of the problem and the number of subproblems. The process of preconditioning iscompletely parallel.

关 键 词：椭圆型方程 区域分裂法 最佳预处理 

分 类 号：O241.82[理学—计算数学]