Tuesday, September 26

Invited Lecture: Reduced Order Methods for Optimisation and Flow Control Parametric Problems in Marine Science and Engineering

Time: 17:30 - 18:30
Room: L1, Building L
Chair: Michael Ulbrich, Technische Universität München

In this work we propose reduced order methods as a suitable approach to face parametrized optimal control problems governed by partial differential equations, with applications in environmental marine sciences and engineering. Environmental parametrized optimal control problems are usually studied for different configurations described by several physical and/or geometrical parameters representing different phenomena. Treating this kind of issue requires a demanding computational effort. Reduced basis techniques are a reliable and rapid tool to solve them, in order to save computational costs in time and memory. After a brief introduction to general parametrized linear quadratic optimal control problems, exploiting their saddle-point structure and a POD-Galerkin sampling and projection algorithm, we propose two applications: a pollutant control in the Gulf of Trieste, Italy and a solution tracking governed by quasi-geostrophic equations describing North Atlantic Ocean dynamic. The two experiments underline how reduced order methods may be a reliable and convenient tool to manage several environmental optimal control problems, differing in equations used, geographical scale and physical meaning. Time permitting some parametric shape optimisation problems in naval and nautical engineering will be shown, as well as reduction techniques in the parameter space.

This is a joint work with Maria Strazzullo, Francesco Ballarin for the optimal flow control and Andrea Mola, Filippo Salmoiraghi and Marco Tezzele for shape optimisation.

Gianluigi Rozza
SISSA Trieste