非协调区域分解的Lagrangian乘子法

§1.引言 近年来随着并行计算机的迅速发展,求解椭圆型方程的区域分解法愈来愈引起人们的兴趣和重视.但是,目前能够见到的有限元区域分解法几乎都要求有限元空间在跨过子区域的边界时是协调的,必然限制有限元区域分解算法的优越性. [3]提出了一种非协凋区域分解法——非协调区域分解的杂交法.采用简化杂交法处理各子区域交界处的非协调性,这种方法在子区域的内部和边界采用两套不同的变量,允许内部变量在跨过各子区域的边界时不连续.但是这种方法有它的局限性,即要求边界变量在各子区域的顶点处必须保持连续性,这对推广到三维空间的情形带来很大的困难.本文提出一种非协调区域分解的Lagrangian乘子法,引进Lagrangian乘子来处理各子区域交界处的非协调性.这种方法也在子区域内部和边界采用两套不同的变量,它不仅允许内部变量在越过各子区域边界时的非协调性,并且还允许边界变量在各子区域的顶点处可以不连续,这就弥补了[3]的不足.同时,这种算法具有[3]的优点,即在不

THE NON-CONFORMING DOMAIN DECOMPOSITION METHOD FOR ELLIPTIC PROBLEMS WITH LAGRANGIAN MULTIPLIERS

In this paper a new non-conforming domain decomposition rechnique is presented forsolving the second-order symmetric elliptic boundary ralue problems with finite element me-thods. The basic idea is to introduce the Lagrangian multipliers to deal with the non-confor-mity of the interfaces between the subdomains. The resulting algorithms are very well suited toparallel computing environment. It is shown that in a rather general situation the convergencerate of the non-conforming technique is the same as in the conforming case. The conditionnumber of the algebraic system arising from the proposed technique is given.