Newton-Picard-based preconditioning for linear-quadratic optimization problems with time-periodic parabolic PDE constraints (Q2904832)

The authors study two preconditioners for a basic linear iterative splitting method for the numerical solution of linear-quadratic optimization problems with time-periodic parabolic partial differential equation (PDE) constraints. Emphasis is given to the Newton-Picard preconditioners and to the establishment of a mesh-independent convergence result for a basic linear iterative method based on the classical Newton-Picard splitting. The proofs of the individual results are given in a self-contained manner. The paper concludes with some nice numerical results.