Reordering-based Schur complement preconditioners for a class of two-by-two block complex linear systems

This paper presents two efficient Schur complement preconditioners for a class of two-by-two block complex linear systems arising from optimal control with time-periodic parabolic equation. The proposed preconditioners are obtained after reordering the original problem into equivalent 4-by-4 block real systems. The resulting two preconditions can be used to accelerate the convergence rate of Krylov subspace methods (such as GMRES) with large regularization parameters (equal to or greater than 1e - 6) and small regularization parameters (less than 1e - 6), respectively. The spectral properties of the associated preconditioned matrices for the proposed Schur complement preconditioners are studied. Numerical experiments are presented to show the effectiveness of the proposed preconditioners. (c) 2023 Elsevier Ltd. All rights reserved.