基于几何非协调分解的Lagrange乘子区域分解方法

A DOMAIN DECOMPOSITION METHOD WITH LAGRANGE MULTIPLIERS BASED ON GEOMETRICALLY NON-CONFORMING DECOMPOSITIONS

本文考虑将Lagrange乘子区域分解方法应用于几何非协调分解的情况来求解二阶椭圆问题,由于采用几何非协调区域分解,每个局部乘子空间关联到多个界面,我们按照一定的规则选取合适的乘子面来定义乘子空间,利用局部正则化技巧,可以消去内部变量,得到关于Lagrange乘子的界面方程,采用一种经济的预条件迭代方法求解界面方程,且相关的预条件子是可扩展的。

In this paper, a domain decomposition method with Lagrange multipliers based on geometrically non-conforming subdomain partitions is considered to solve second order elliptic problems. Because of the geometrically non-conforming decompositions, every local multi- plier space is relatted with two interfaces at least, and appropriate multiplier faces should be chosen. Using the local regularization technique, we can build the interface equation of the Lagrange multipliers by eliminating the interior variables in every subdomain. A cheap preconditioned iterative method is developed to solve the interface equation, and the corresponding preconditioner is scalable.