一类求解鞍点问题的广义不精确Uzawa方法  

A CLASS OF GENERALIZED INEXACT UZAWA METHODS FOR SADDLE POINT PROBLEMS

作　　者：豆铨煜[1] 殷俊锋[2] 

机构地区：[1]周口师范学院数学系,河南周口466001 [2]同济大学应用数学系,上海200092

出　　处：《计算数学》2012年第1期37-48,共12页Mathematica Numerica Sinica

基　　金：国家自然科学基金(10801106);中央高校基本科研业务费专项资金

摘　　要：本文提出了一类求解大型稀疏鞍点问题的新的广义不精确Uzawa算法.该方法不仅可以包含前人的方法,而且可以拓展出很多新方法.理论分析给出该方法收敛的条件,并详细的分析了其收敛性质和参数矩阵的选取方法.通过对有限元离散的Stokes问题的数值实验表明,新方法是行之有效的,其收敛速度明显优于原来的算法.A class of general inexact Uzawa methods for the solution of large and sparse saddle point problems are presented, which can not only cover many existing approaches, but also imply many new iteration scheme. Theoretical analyses give the convergence condition for new methods, as well as the choice of the optimal parameter matrices. Numerical results from discrete stokes problems by finite element method show that the new algorithm is efficient, and much faster than existing algorithms.

关 键 词：鞍点问题 Uzawa方法 预处理 收敛性 

分 类 号：O241.6[理学—计算数学]