A DOMAIN DECOMPOSITION METHOD WITH LAGRANGE MULTIPLIERS BASED ON GEOMETRICALLY NON-CONFORMING DECOMPOSITIONS
基于几何非协调分解的Lagrange乘子区域分解方法

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 multiplier 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.