基于子结构法构造用非协调元解椭圆型问题的预处理器（Ⅰ）  

THE CONSTRUCTION OF PRECONDITIONERS FOR ELLIPTIC PROBLEMS DISCRETIZED BY NONCONFORMING FINITE ELEMENTS VIA SUBSTRUCTURING(Ⅰ)

作　　者：顾金生[1] 胡显承[1] 

机构地区：[1]清华大学应用数学系

出　　处：《计算数学》1996年第2期113-128,共16页Mathematica Numerica Sinica

基　　金：国家自然科学基金

摘　　要：基于子结构法构造用非协调元解椭圆型问题的预处理器（Ⅰ）顾金生，胡显承（清华大学应用数学系）ＴＨＥＣＯＮＳＴＲＵＣＴＩＯＮＯＦＰＲＥＣＯＮＤＩＴＩＯＮＥＲＳＦＯＲＥＬＬＩＰＴＩＣＰＲＯＢＬＥＭＳＤＩＳＣＲＥＴＩＺＥＤＢＹＮＯＮＣＯＮＦＯＲＭＩＮＧＦＩＮ...Abstract We consider the problem of solving the algebraic system of equations which arise from the discretisation of symmetric elliptic problems via a class of nonconforming finite elements, which is only continuous at the nodes of the quasi-uniform mesh. The condition number of the algebraic system is proved to be O(h-2), where h is the mesh parameter. By substructuring (also known as nonoverlap domain decomposition), we proposed a series of preconditioners. The resulting preconditioned algorithms are well suited to emerging parallel computing architectures. A basic theory for the analysis of the condition number of the preconditioned system (which determines the iterative convergence rate of the algorithm) is presented. The condition number of our preconditioned system is,where H is the maximum diameter of subdomains.

关 键 词：子结构法 非协调元 椭圆型问题 预处理器 

分 类 号：O241.82[理学—计算数学]