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• W1971937117 abstract "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." @default.
• W1971937117 created "2016-06-24" @default.
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• W1971937117 date "2012-01-01" @default.
• W1971937117 modified "2023-10-14" @default.
• W1971937117 title "Newton–Picard-Based Preconditioning for Linear-Quadratic Optimization Problems with Time-Periodic Parabolic PDE Constraints" @default.
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• W1971937117 doi "https://doi.org/10.1137/100807776" @default.
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