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.
|Nome||LECTURE NOTES IN COMPUTATIONAL SCIENCE AND ENGINEERING|
|Convegno||European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019|
|Città||Egmond aan Zee, The Netherlands|
|Periodo||30/9/19 → 4/10/19|
- Reduced Order Methods
- Time Dependent Optimal Flow Control Problems