TY - CONF T1 - Reduced Order Methods for Parametrized Non-linear and Time Dependent Optimal Flow Control Problems, Towards Applications in Biomedical and Environmental Sciences T2 - Numerical Mathematics and Advanced Applications ENUMATH 2019 Y1 - 2021 A1 - Maria Strazzullo A1 - Zakia Zainib A1 - F. Ballarin A1 - Gianluigi Rozza ED - Fred J Vermolen ED - Cornelis Vuik AB -

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.

JF - Numerical Mathematics and Advanced Applications ENUMATH 2019 PB - Springer International Publishing CY - Cham SN - 978-3-030-55874-1 UR - https://www.springerprofessional.de/en/reduced-order-methods-for-parametrized-non-linear-and-time-depen/19122676 ER -