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

TitleReduced Order Methods for Parametrized Non-linear and Time Dependent Optimal Flow Control Problems, Towards Applications in Biomedical and Environmental Sciences
Publication TypeConference Paper
Year of Publication2021
AuthorsStrazzullo, M, Zainib, Z, Ballarin, F, Rozza, G
EditorVermolen, FJ, Vuik, C
Conference NameNumerical Mathematics and Advanced Applications ENUMATH 2019
Date Published2021//
PublisherSpringer International Publishing
Conference LocationCham
ISBN Number978-3-030-55874-1
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.

URLhttps://www.springerprofessional.de/en/reduced-order-methods-for-parametrized-non-linear-and-time-depen/19122676
DOI10.1007/978-3-030-55874-1_83

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