Some notes concerning preconditioning of linear parabolic optimal control problems
Year: 2024
Type: preprint
Abstract: In this paper we study the conditioning of optimal control problems constrained by linear parabolic equations with Neumann boundary conditions. While we concentrate on a given end-time target function the results hold also when the target function is given over the whole time horizon. When implicit time discretization and conforming finite elements in space are employed we show that the reduced problem formulation has condition numbers which are bounded independently of the discretization level in arbitrary space dimension. In addition we propose for the all-at-once approach, i.e. for the first-order conditions of the unreduced system a preconditioner based on work by Greif and Schötzau, which provides also bounds on the eigenvalue distribution independently of the discretization level. Numerical experiments demonstrate the obtained results and the efficiency of the suggested preconditioners.
Source: arXiv (Cornell University)
Author: Blank, Luise
Institution: University of Regensburg
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6929253998
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