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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 Publication2020
AuthorsStrazzullo, M, Zainib, Z, Ballarin, F, Rozza, G
Conference NameENUMATH2019 proceedings
PublisherSpringer
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, optimal control problems require a huge computational effort in order to be solved, most of all in a physical and/or geometrical parametrized setting. Reduced order methods are a reliably 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 exploit POD-Galerkin reduction over a parametrized optimality system, derived from Karush-Kuhn-Tucker conditions. The methodology presented is tested on two boundary control problems, governed respectively by (i) time dependent Stokes equations and (ii) steady non-linear Navier-Stokes equations.

URLhttps://arxiv.org/abs/1912.07886

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