非重迭型区域分解预处理共轭梯度法

A PRECONDITIONED CONJUGATE GRADIENT METHO D WITH NONOVERLAP DOMAIN DECOMPOSITION

本文讨论含有内部交叉点(cross point)的非重迭型区域分解预处理共轭梯度法。称一个点是交叉点,如果有三个或三个以上的子区域以该点做为共同边界点,该点为区域内点。 本文根据在对称正定块对角矩阵类中对角块是对称正定矩阵比较有效的预处理器的理论,通过简单自然的刚度矩阵分裂,基于代数方式。

In this paper, a preconditioned conjugate gradient method with nonoverlap domain decom-position is considered. Based on the algebraic approach, a preconditioner is given by splittingthe stiff matrix; The matrix form of this preconditioner is presented. The condition numberof the preconditioned system is proportion to C (1+ln (H/h))~2, where H is the maximum dia-meter of subdomains and h is the parameter of the finite element.