Publikation: Model Order Reduction by Proper Orthogonal Decomposition
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2020
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BENNER, Peter, ed. and others. Model Order Reduction : Volume 2 Snapshot-Based Methods and Algorithms. Berlin: De Gruyter, 2020, pp. 47-96. ISBN 978-3-11-067140-7. Available under: doi: 10.1515/9783110671490-002
Zusammenfassung
We provide an introduction to proper orthogonal decomposition (POD) model order reduction with focus on (nonlinear) parametric partial differential equations (PDEs) and (nonlinear) time-dependent PDEs, and PDE-constrained optimization with POD surrogate models as application. We cover the relation of POD and singular value decomposition, POD from the infinite-dimensional perspective, reduction of nonlinearities, certification with a priori and a posteriori error estimates, spatial and temporal adaptivity, input dependency of the POD surrogate model, POD basis update strategies in optimal control with surrogate models, and sketch related algorithmic frameworks. The perspective of the method is demonstrated with several numerical examples.
Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
510 Mathematik
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POD model order reduction, (discrete) empirical interpolation, adaptivity, parametric PDEs, evolutionary PDEs, certification with error analysis
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GRÄSSLE, Carmen, Michael HINZE, Stefan VOLKWEIN, 2020. Model Order Reduction by Proper Orthogonal Decomposition. In: BENNER, Peter, ed. and others. Model Order Reduction : Volume 2 Snapshot-Based Methods and Algorithms. Berlin: De Gruyter, 2020, pp. 47-96. ISBN 978-3-11-067140-7. Available under: doi: 10.1515/9783110671490-002BibTex
@incollection{Grale2020Model-44977.2,
year={2020},
doi={10.1515/9783110671490-002},
title={Model Order Reduction by Proper Orthogonal Decomposition},
isbn={978-3-11-067140-7},
publisher={De Gruyter},
address={Berlin},
booktitle={Model Order Reduction : Volume 2 Snapshot-Based Methods and Algorithms},
pages={47--96},
editor={Benner, Peter},
author={Gräßle, Carmen and Hinze, Michael and Volkwein, Stefan}
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