01664nas a2200181   4500008004100000020002200041245016600063210006900229260005200298520089600350100002201246700001801268700001701286700002101303700002201324700001901346856011701365       2021                        eng d  a978-3-030-55874-100aReduced Order Methods for Parametrized Non-linear and Time Dependent Optimal Flow Control Problems, Towards Applications in Biomedical and Environmental Sciences0 aReduced Order Methods for Parametrized Nonlinear and Time Depend  aChambSpringer International Publishingc2021//3 a<p>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.</p>1 aStrazzullo, Maria1 aZainib, Zakia1 aBallarin, F.1 aRozza, Gianluigi1 aVermolen, Fred, J1 aVuik, Cornelis  uhttps://www.springerprofessional.de/en/reduced-order-methods-for-parametrized-non-linear-and-time-depen/19122676