Inexact solvers for saddle-point system arising from domain decomposition of linear elasticity problems in three dimensions
X. Chen 1, Q. Hu 21 Department of Applied Mathematics, College of Computer and Information Engineering, Beijing Technology and Business University, Beijing 100048, China.
2 LSEC, Institute of Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, CAS, Beijing 100190, China.
Received by the editors March 2, 2009 and, in revised form, May 26, 2010.
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.AMS subject classifications: 65F10, 65N30, 65N55
Key words: Domain decomposition, geometrically non-conforming, Lagrange multiplier, saddle-point system, preconditioners, condition number.
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