TY - JOUR
T1 - Overlapping Domain Decomposition Preconditioners for Unconstrained Elliptic Optimal Control Problems
AU - Zhiyu Tan, Wei Gong & Ningning Yan
JO - International Journal of Numerical Analysis and Modeling
VL - 4-5
SP - 550
EP - 570
PY - 2017
DA - 2017/08
SN - 14
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/10049.html
KW - Overlapping domain decomposition method, elliptic optimal control problem, preconditioned MINRES method, preconditioned GMRES method.
AB - <p style="text-align: justify;">In this paper, we propose several overlapping domain decomposition preconditioners
for solving the unconstrained elliptic optimal control problem, based on the two level additive
Schwarz algorithm. We consider the cases with controls on the whole domain and controls from
a local subset. The latter case can be viewed as the subproblems when we solve the control-constrained
control problem by using semi-smooth Newton method. When the controls act on
the whole domain, we construct a symmetric and positive definite preconditioner which is proved
to be robust combined with preconditioned MINRES method, and a symmetric and indefinite
preconditioner which can be used in the preconditioned GMRES method and shows better numerical
performance than the positive definite one. When the controls act on a local subset, we
also construct a similar symmetric and indefinite preconditioner, the numerical experiments show
its efficiency when combined with preconditioned GMRES method.</p>