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

Francesco Ballarin, Maria Strazzullo, Zakia Zainib, Gianluigi Rozza

Risultato della ricerca: Contributo in libroContributo a convegno

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.
Lingua originaleEnglish
Titolo della pubblicazione ospiteLecture Notes in Computational Science and Engineering
Pagine841-850
Numero di pagine10
Volume139
DOI
Stato di pubblicazionePubblicato - 2021
EventoEuropean Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019 - Egmond aan Zee, The Netherlands
Durata: 30 set 20194 ott 2019

Serie di pubblicazioni

NomeLECTURE NOTES IN COMPUTATIONAL SCIENCE AND ENGINEERING

Convegno

ConvegnoEuropean Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019
CittàEgmond aan Zee, The Netherlands
Periodo30/9/194/10/19

Keywords

  • Reduced Order Methods
  • Time Dependent Optimal Flow Control Problems

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