GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Deflation of conjugate gradients with applications to boundary value problems
SIAM Journal on Numerical Analysis
Stabilization of unstable procedures: the recursive projection method
SIAM Journal on Numerical Analysis
A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
Deflation Techniques for an Implicitly Restarted Arnoldi Iteration
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Scientific Computing
Optimal Control of Linear Periodic Resonant Systems in Hilbert Spaces
SIAM Journal on Control and Optimization
An Adaptive Newton--Picard Algorithm with Subspace Iteration for Computing Periodic Solutions
SIAM Journal on Scientific Computing
A Deflation Technique for Linear Systems of Equations
SIAM Journal on Scientific Computing
A Note on Preconditioning for Indefinite Linear Systems
SIAM Journal on Scientific Computing
On the Solution of Equality Constrained Quadratic Programming Problems Arising in Optimization
SIAM Journal on Scientific Computing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Multigrid methods for parabolic distributed optimal control problems
Journal of Computational and Applied Mathematics
Aerodynamic shape optimization using simultaneous pseudo-timestepping
Journal of Computational Physics
SIAM Journal on Matrix Analysis and Applications
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Nested multigrid methods for time-periodic, parabolic optimal control problems
Computing and Visualization in Science
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We develop and investigate two preconditioners for a basic linear iterative splitting method for the numerical solution of linear-quadratic optimization problems with time-periodic parabolic PDE constraints. The resulting real-valued linear system to be solved is symmetric indefinite. We propose all-at-once symmetric indefinite preconditioners based on a Newton-Picard approach which divides the variable space into slow and fast modes. The division is performed either classically with eigenspace methods or with a novel two-grid approach. We prove mesh-independent convergence for the classical Newton-Picard preconditioner, present a complexity analysis, and show numerical results for the classical and the two-grid preconditioners. Moreover, the preconditioners compare favorably with existing symmetric positive definite Schur complement preconditioners in a Krylov method context.