@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.}
}