@TechReport{ it:2015-030,
author = {Owe Axelsson and Shiraz Farouq and Maya Neytcheva},
title = {Comparison of preconditioned {K}rylov subspace iteration
methods for {PDE}-constrained optimization problems.
{S}tokes control},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Scientific Computing},
year = {2015},
number = {2015-030},
month = sep,
abstract = {The governing dynamics of fluid flow is stated as a system
of partial differential equations referred to as the
Navier-Stokes system. In industrial and scientific
applications, fluid flow control becomes an optimization
problem where the governing partial differential equations
of the fluid flow are stated as constraints. When
discretized, the optimal control of the Navier-Stokes
equations leads to large sparse saddle point systems in two
levels.
In this paper we consider distributed optimal control for
the Stokes system and test the particular case when the
arising linear system can be compressed after eliminating
the control function. In that case, a system arises in a
form which enables the application of an efficient block
matrix preconditioner that previously has been applied to
solve complex-valued systems in real arithmetic. Under
certain conditions the condition number of the so
preconditioned matrix is bounded by 2. The numerical and
computational efficiency of the method in terms of number
of iterations and execution time is favorably compared with
other published methods.}
}