A rational deferred correction approach to PDE-constrained optimization

Güttel, Stefan and Pearson, John W. (2016) A rational deferred correction approach to PDE-constrained optimization. [MIMS Preprint]

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Abstract

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: MIMS Preprint
Uncontrolled Keywords: PDE-constrained optimization, deferred correction, time-dependent PDE, coupled system
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 34 Ordinary differential equations
MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
MSC 2010, the AMS's Mathematics Subject Classification > 93 Systems theory; control
Depositing User: Stefan Güttel
Date Deposited: 28 Sep 2016
Last Modified: 08 Nov 2017 18:18
URI: https://eprints.maths.manchester.ac.uk/id/eprint/2505

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