@TechReport{ it:2017-014,
author = {Zhao-Zheng Liang and Owe Axelsson and Maya Neytcheva},
title = {A Robust Structured Preconditioner for Time-Harmonic
Parabolic Optimal Control Problems},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Scientific Computing},
year = {2017},
number = {2017-014},
month = aug,
abstract = {We consider the iterative solution of optimal control
problems constrained by the time-harmonic parabolic
equations. Due to the time-harmonic property of the control
equations, a suitable discretization of the corresponding
optimality systems leads to a large complex linear system
with special two-by-two block matrix of saddle point form.
For this algebraic system, an efficient preconditioner is
constructed, which results in a fast Krylov subspace
solver, that is robust with respect to the mesh size,
frequency and regularization parameters. Furthermore, the
implementation is straightforward and the computational
complexity is of optimal order, linear in the number of
degrees of freedom. We show that the eigenvalue
distribution of the corresponding preconditioned matrix
leads to a condition number bounded above by 2. Numerical
experiments confirming the theoretical derivations are
presented, including comparisons with some other existing
preconditioners.}
}