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Abstract
The accurate and ecient 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.
Original language | English |
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Pages (from-to) | 1861-1892 |
Number of pages | 26 |
Journal | IMA Journal of Numerical Analysis |
Volume | 38 |
Issue number | 4 |
Early online date | 7 Oct 2017 |
DOIs | |
Publication status | Published - 16 Oct 2018 |
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Dive into the research topics of 'A rational deferred correction approach to parabolic optimal control problems'. Together they form a unique fingerprint.Projects
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John Pearson
- School of Mathematics - Personal Chair of Scientific Computing
Person: Academic: Research Active (Teaching)