Model Reduction For Parametrized Optimal Control Problems in Environmental Marine Sciences and Engineering
We propose reduced order methods as a suitable approach to face parametrized optimal control problems governed by partial differential equations, with applications in en- vironmental marine sciences and engineering. Environmental parametrized optimal control problems are usually studied for differen...
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ftdatacite:10.48550/arxiv.1710.01640 2023-05-15T17:33:45+02:00 Model Reduction For Parametrized Optimal Control Problems in Environmental Marine Sciences and Engineering Strazzullo, Maria Ballarin, Francesco Mosetti, Renzo Rozza, Gianluigi 2017 https://dx.doi.org/10.48550/arxiv.1710.01640 https://arxiv.org/abs/1710.01640 unknown arXiv arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Numerical Analysis math.NA Optimization and Control math.OC FOS Mathematics Preprint Article article CreativeWork 2017 ftdatacite https://doi.org/10.48550/arxiv.1710.01640 2022-04-01T10:26:37Z We propose reduced order methods as a suitable approach to face parametrized optimal control problems governed by partial differential equations, with applications in en- vironmental marine sciences and engineering. Environmental parametrized optimal control problems are usually studied for different configurations described by several physical and/or geometrical parameters representing different phenomena and structures. The solution of parametrized problems requires a demanding computational effort. In order to save com- putational time, we rely on reduced basis techniques as a reliable and rapid tool to solve parametrized problems. We introduce general parametrized linear quadratic optimal control problems, and the saddle-point structure of their optimality system. Then, we propose a POD-Galerkin reduction of the optimality system. Finally, we test the resulting method on two environmental applications: a pollutant control in the Gulf of Trieste, Italy and a solution tracking governed by quasi-geostrophic equations, in its linear and nonlinear version, describing North Atlantic Ocean dynamic. The two experiments underline how reduced order methods are a reliable and convenient tool to manage several environmental optimal control problems, for different mathematical models, geographical scale as well as physical meaning. : A section 5 concerning the optimal control governed by nonlinear quasi-geostrophic equations has been added Report North Atlantic DataCite Metadata Store (German National Library of Science and Technology) Saddle Point ENVELOPE(73.483,73.483,-53.017,-53.017) |
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DataCite Metadata Store (German National Library of Science and Technology) |
op_collection_id |
ftdatacite |
language |
unknown |
topic |
Numerical Analysis math.NA Optimization and Control math.OC FOS Mathematics |
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Numerical Analysis math.NA Optimization and Control math.OC FOS Mathematics Strazzullo, Maria Ballarin, Francesco Mosetti, Renzo Rozza, Gianluigi Model Reduction For Parametrized Optimal Control Problems in Environmental Marine Sciences and Engineering |
topic_facet |
Numerical Analysis math.NA Optimization and Control math.OC FOS Mathematics |
description |
We propose reduced order methods as a suitable approach to face parametrized optimal control problems governed by partial differential equations, with applications in en- vironmental marine sciences and engineering. Environmental parametrized optimal control problems are usually studied for different configurations described by several physical and/or geometrical parameters representing different phenomena and structures. The solution of parametrized problems requires a demanding computational effort. In order to save com- putational time, we rely on reduced basis techniques as a reliable and rapid tool to solve parametrized problems. We introduce general parametrized linear quadratic optimal control problems, and the saddle-point structure of their optimality system. Then, we propose a POD-Galerkin reduction of the optimality system. Finally, we test the resulting method on two environmental applications: a pollutant control in the Gulf of Trieste, Italy and a solution tracking governed by quasi-geostrophic equations, in its linear and nonlinear version, describing North Atlantic Ocean dynamic. The two experiments underline how reduced order methods are a reliable and convenient tool to manage several environmental optimal control problems, for different mathematical models, geographical scale as well as physical meaning. : A section 5 concerning the optimal control governed by nonlinear quasi-geostrophic equations has been added |
format |
Report |
author |
Strazzullo, Maria Ballarin, Francesco Mosetti, Renzo Rozza, Gianluigi |
author_facet |
Strazzullo, Maria Ballarin, Francesco Mosetti, Renzo Rozza, Gianluigi |
author_sort |
Strazzullo, Maria |
title |
Model Reduction For Parametrized Optimal Control Problems in Environmental Marine Sciences and Engineering |
title_short |
Model Reduction For Parametrized Optimal Control Problems in Environmental Marine Sciences and Engineering |
title_full |
Model Reduction For Parametrized Optimal Control Problems in Environmental Marine Sciences and Engineering |
title_fullStr |
Model Reduction For Parametrized Optimal Control Problems in Environmental Marine Sciences and Engineering |
title_full_unstemmed |
Model Reduction For Parametrized Optimal Control Problems in Environmental Marine Sciences and Engineering |
title_sort |
model reduction for parametrized optimal control problems in environmental marine sciences and engineering |
publisher |
arXiv |
publishDate |
2017 |
url |
https://dx.doi.org/10.48550/arxiv.1710.01640 https://arxiv.org/abs/1710.01640 |
long_lat |
ENVELOPE(73.483,73.483,-53.017,-53.017) |
geographic |
Saddle Point |
geographic_facet |
Saddle Point |
genre |
North Atlantic |
genre_facet |
North Atlantic |
op_rights |
arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
op_doi |
https://doi.org/10.48550/arxiv.1710.01640 |
_version_ |
1766132359788232704 |