Reduced order methods for parametrized non-linear and time dependent optimal flow control problems, towards applications in biomedical and environmental sciences

Journal: 

Inbook: ENUMATH2019 proceedings

Date: 

2020

Authors: 

Maria Strazzullo and Zakia Zainib and Francesco Ballarin and Gianluigi Rozza

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.

 

@inproceedings{StrazzulloZainibBallarinRozza2020,
author = {Maria Strazzullo and Zakia Zainib and Francesco Ballarin and Gianluigi Rozza},
title = {Reduced order methods for parametrized non-linear and time dependent optimal flow control problems, towards applications in biomedical and environmental sciences},
year = {2020},
booktitle = {ENUMATH2019 proceedings},
publisher = {Springer},
}