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A rational deferred correction approach to parabolic optimal control problems

Güttel, Stefan, Pearson, John W (2018) A rational deferred correction approach to parabolic optimal control problems. IMA Journal of Mathematical Control and Information, 38 (4). pp. 1861-1892. ISSN 0265-0754. E-ISSN 1471-6887. (doi:10.1093/imanum/drx046) (KAR id:54209)

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The accurate and efficient solution of time-dependent PDE-constrained optimization problems is a challenging task, in large part due to the very high dimension of the matrix systems that need to be solved. We devise a new deferred correction method for coupled systems of time-dependent PDEs, allowing one to iteratively improve the accuracy of low-order time stepping schemes. We consider two variants of our method, a splitting and a coupling version, and analyze their convergence properties. We then test our approach on a number of PDE-constrained optimization problems. We obtain solution accuracies far superior to that achieved when solving a single discretized problem, in particular in cases where the accuracy is limited by the time discretization. Our approach allows for the direct reuse of existing solvers for the resulting matrix systems, as well as state-of-the-art preconditioning strategies.

Item Type: Article
DOI/Identification number: 10.1093/imanum/drx046
Uncontrolled keywords: PDE-constrained optimization; deferred correction; time-dependent PDE; coupled system
Subjects: Q Science > QA Mathematics (inc Computing science) > QA297 Numerical analysis
Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: John Pearson
Date Deposited: 15 Feb 2016 17:05 UTC
Last Modified: 16 Feb 2021 13:33 UTC
Resource URI: (The current URI for this page, for reference purposes)
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