Liu, Jun; Pearson, John W. Parameter-robust preconditioning for the optimal control of the wave equation. (English) Zbl 07171737 Numer. Algorithms 83, No. 3, 1171-1203 (2020). Summary: In this paper, we propose and analyze a new matching-type Schur complement preconditioner for solving the discretized first-order necessary optimality conditions that characterize the optimal control of wave equations. Coupled with this is a recently developed second-order implicit finite difference scheme used for the full space-time discretization of the optimality system of PDEs. Eigenvalue bounds for the preconditioned system are derived, which provide insights into the convergence rates of the preconditioned Krylov subspace method applied. Numerical examples are presented to validate our theoretical analysis and demonstrate the effectiveness of the proposed preconditioner, in particular its robustness with respect to very small regularization parameters, and all mesh sizes in the spatial variables. Cited in 5 Documents MSC: 65-XX Numerical analysis Keywords:preconditioning; optimal control; wave equation; finite difference method; Schur complement; regularization; saddle-point system Software:IFISS PDFBibTeX XMLCite \textit{J. Liu} and \textit{J. W. Pearson}, Numer. Algorithms 83, No. 3, 1171--1203 (2020; Zbl 07171737) Full Text: DOI Link References: [1] Borzì, A.; Kunisch, K.; Kwak, Dy, Accuracy and convergence properties of the finite difference multigrid solution of an optimal control optimality system, SIAM J. 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