We introduce reduced order methods as an efficient strategy to solve parametrized non-linear and time dependent optimal flow control problems governed by partial differential equations. Indeed, the optimal control problems require a huge computational effort in order to be solved, most of all in physical and/or geometrical parametrized settings. Reduced order methods are a reliable and suitable approach, increasingly gaining popularity, to achieve rapid and accurate optimal solutions in several fields, such as in biomedical and environmental sciences. In this work, we employ a POD-Galerkin reduction approach over a parametrized optimality system, derived from the Karush-Kuhn-Tucker conditions. The methodology presented is tested on two boundary control problems, governed respectively by (1) time dependent Stokes equations and (2) steady non-linear Navier-Stokes equations.

Reduced Order Methods for Parametrized Non-linear and Time Dependent Optimal Flow Control Problems, Towards Applications in Biomedical and Environmental Sciences / Strazzullo, Maria; Zainib, Zakia; Ballarin, Francesco; Rozza, Gianluigi. - 139:(2021), pp. 841-850. ((Intervento presentato al convegno European Conference, Egmond aan Zee tenutosi a The Netherlands nel 30/09/2019 - 04/10/2019 [10.1007/978-3-030-55874-1_83].

Reduced Order Methods for Parametrized Non-linear and Time Dependent Optimal Flow Control Problems, Towards Applications in Biomedical and Environmental Sciences

Strazzullo, Maria;Zainib, Zakia;Ballarin, Francesco;Rozza, Gianluigi
2021

Abstract

We introduce reduced order methods as an efficient strategy to solve parametrized non-linear and time dependent optimal flow control problems governed by partial differential equations. Indeed, the optimal control problems require a huge computational effort in order to be solved, most of all in physical and/or geometrical parametrized settings. Reduced order methods are a reliable and suitable approach, increasingly gaining popularity, to achieve rapid and accurate optimal solutions in several fields, such as in biomedical and environmental sciences. In this work, we employ a POD-Galerkin reduction approach over a parametrized optimality system, derived from the Karush-Kuhn-Tucker conditions. The methodology presented is tested on two boundary control problems, governed respectively by (1) time dependent Stokes equations and (2) steady non-linear Navier-Stokes equations.
Numerical Mathematics and Advanced Applications ENUMATH 2019
139
841
850
978-3-030-55873-4
https://arxiv.org/abs/1912.07886
Springer
Strazzullo, Maria; Zainib, Zakia; Ballarin, Francesco; Rozza, Gianluigi
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/123375
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