TY - JOUR
T1 - Inexact Solvers for Saddle-Point System Arising from Domain Decomposition of Linear Elasticity Problems in Three Dimensions
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 156
EP - 173
PY - 2011
DA - 2011/08
SN - 8
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/679.html
KW - Domain decomposition, geometrically non-conforming, Lagrange multiplier, saddle-point system, preconditioners, condition number.
AB - <p style="text-align: justify;">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.</p>