In the present paper we propose reduced order methods as a reliable strategy to efficiently solve parametrized optimal control problems governed by shallow waters equations in a solution tracking setting. The physical parametrized model we deal with is nonlinear and time dependent: this leads to very time consuming simulations which can be unbearable, e.g., in a marine environmental monitoring plan application. Our aim is to show how reduced order modelling could help in studying different configurations and phenomena in a fast way. After building the optimality system, we rely on a POD-Galerkin reduction in order to solve the optimal control problem in a low dimensional reduced space. The presented theoretical framework is actually suited to general nonlinear time dependent optimal control problems. The proposed methodology is finally tested with a numerical experiment: the reduced optimal control problem governed by shallow waters equations reproduces the desired velocity and height profiles faster than the standard model, still remaining accurate.

POD-Galerkin model order reduction for parametrized nonlinear time-dependent optimal flow control: an application to shallow water equations / Strazzullo, Maria; Ballarin, Francesco; Rozza, Gianluigi. - In: JOURNAL OF NUMERICAL MATHEMATICS. - ISSN 1569-3953. - 30:1(2022), pp. 63-84. [10.1515/jnma-2020-0098]

POD-Galerkin model order reduction for parametrized nonlinear time-dependent optimal flow control: an application to shallow water equations

Maria Strazzullo;Francesco Ballarin;Gianluigi Rozza
2022

Abstract

In the present paper we propose reduced order methods as a reliable strategy to efficiently solve parametrized optimal control problems governed by shallow waters equations in a solution tracking setting. The physical parametrized model we deal with is nonlinear and time dependent: this leads to very time consuming simulations which can be unbearable, e.g., in a marine environmental monitoring plan application. Our aim is to show how reduced order modelling could help in studying different configurations and phenomena in a fast way. After building the optimality system, we rely on a POD-Galerkin reduction in order to solve the optimal control problem in a low dimensional reduced space. The presented theoretical framework is actually suited to general nonlinear time dependent optimal control problems. The proposed methodology is finally tested with a numerical experiment: the reduced optimal control problem governed by shallow waters equations reproduces the desired velocity and height profiles faster than the standard model, still remaining accurate.
30
1
63
84
https://arxiv.org/abs/2003.09695
Strazzullo, Maria; Ballarin, Francesco; Rozza, Gianluigi
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/128550
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