Inexact Solvers for Saddle-point System Arising from Domain Decomposition of Linear Elasticity Problems in Three Dimensions

In this paper, a domain decomposition method with lagrange mul-tipliers based on geometrically non-conforming subdomain partitions for three dimensional linear elasticity is considered. Because of the geometrically non-conforming partitions, appropriate multiplier spaces should be chosen, and a saddle-point system is then built. An aug-mented technique is introduced, such that the resulting new saddle-point system can be solved by the existing iterative methods. Two simple inexact preconditioners are constructed for the saddle-point sys-tem, one for the displacement variable, and the other for the Schur com-plement associated with the multiplier variable. It is shown that the global preconditioned system has a nearly optimal condition number, which is independent of the large variations of the material parameters across the local interfaces