Publikation: Reduced basis model order reduction in optimal control of a nonsmooth semilinear elliptic PDE
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2022
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HERZOG, Roland, ed., Matthias HEINKENSCHLOSS, ed., Dante KALISE, ed. and others. Optimization and Control for Partial Differential Equations : Uncertainty quantification, open and closed-loop control, and shape optimization. Berlin: De Gruyter, 2022, pp. 1-32. Radon Series on Computational and Applied Mathematics. 29. ISBN 978-3-11-069596-0. Available under: doi: 10.1515/9783110695984-001
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In this paper, an optimization problem governed by a nonsmooth semilinear elliptic partial differential equation is considered. A reduced order approach is applied in order to obtain a computationally fast and certified numerical solution approach. Using the reduced basis method and efficient a-posteriori error estimation for the primal and dual equations, an adaptive algorithm is developed and tested successfully for several numerical examples.
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510 Mathematik
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BERNREUTHER, Marco, Georg MÜLLER, Stefan VOLKWEIN, 2022. Reduced basis model order reduction in optimal control of a nonsmooth semilinear elliptic PDE. In: HERZOG, Roland, ed., Matthias HEINKENSCHLOSS, ed., Dante KALISE, ed. and others. Optimization and Control for Partial Differential Equations : Uncertainty quantification, open and closed-loop control, and shape optimization. Berlin: De Gruyter, 2022, pp. 1-32. Radon Series on Computational and Applied Mathematics. 29. ISBN 978-3-11-069596-0. Available under: doi: 10.1515/9783110695984-001BibTex
@incollection{Bernreuther2022Reduc-49208.3,
year={2022},
doi={10.1515/9783110695984-001},
title={Reduced basis model order reduction in optimal control of a nonsmooth semilinear elliptic PDE},
number={29},
isbn={978-3-11-069596-0},
publisher={De Gruyter},
address={Berlin},
series={Radon Series on Computational and Applied Mathematics},
booktitle={Optimization and Control for Partial Differential Equations : Uncertainty quantification, open and closed-loop control, and shape optimization},
pages={1--32},
editor={Herzog, Roland and Heinkenschloß, Matthias and Kalise, Dante},
author={Bernreuther, Marco and Müller, Georg and Volkwein, Stefan}
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