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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Acknowledgements
The author gratefully acknowledges the financial support by the Academy of Finland under the grant 295897 as well as by the Central Finland regional Fund of the Finnish Cultural Foundation.
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Wolfmayr, M. (2021). Efficient Solvers for Time-Periodic Parabolic Optimal Control Problems Using Two-Sided Bounds of Cost Functionals. In: Vermolen, F.J., Vuik, C. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2019. Lecture Notes in Computational Science and Engineering, vol 139. Springer, Cham. https://doi.org/10.1007/978-3-030-55874-1_120
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