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2021 | OriginalPaper | Chapter

Efficient Solvers for Time-Periodic Parabolic Optimal Control Problems Using Two-Sided Bounds of Cost Functionals

Author : Monika Wolfmayr

Published in: Numerical Mathematics and Advanced Applications ENUMATH 2019

Publisher: Springer International Publishing

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Abstract

This article is devoted to presenting efficient solvers for time-periodic parabolic optimization problems. The solvers are based on deriving two-sided bounds for the cost functional. Here, we especially employ the time-periodic nature of the problem discussed in order to obtain fully computable and guaranteed upper and lower bounds for the cost functional. We present the multiharmonic finite element method as a proper approach for deriving a discretized solution of the time-periodic problem. The multiharmonic finite element functions can be used as initial guess for the arbitrary functions in the upper and lower bounds, which then can be minimized and maximized, respectively, in order to obtain an approximate solution of any desired accuracy. Finally, new numerical results are presented in order to show the efficiency of the method discussed also in practice.

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previous chapter Convergence Rates for Matrix P-Greedy Variants

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Title: Efficient Solvers for Time-Periodic Parabolic Optimal Control Problems Using Two-Sided Bounds of Cost Functionals
Author: Monika Wolfmayr
Publisher: Springer International Publishing
Book: Numerical Mathematics and Advanced Applications ENUMATH 2019
Print ISBN: 978-3-030-55873-4

Electronic ISBN: 978-3-030-55874-1

Copyright Year: 2021
DOI: https://doi.org/10.1007/978-3-030-55874-1_120

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