In this paper, we propose a domain decomposition method with Lagrange
multipliers for three-dimensional linear elasticity, based on geometrically
non-conforming subdomain partitions. Some appropriate multiplier spaces are
presented to deal with the geometrically non-conforming partitions, resulting
in a discrete saddle-point system. An augmented 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 system, one for the displacement variable, and the other for the
Schur complement 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.