Mathematics

The talk aims at introducing reduced order methods in optimal control problems governed by parametrized partial differential equations and at applying them in environmental marine applications. Computationally, optimal control problems are very demanding: a numerical method capable to reduce their dimensionality turns out to be an indispensable tool when several physical and geometrical configurations are involved, as in the  case of natural science and, specifically, marine science.  For this reason, reduced basis methods have been chosen as resolution strategy: they allow parametric optimal control problems to be solved in a rapid and accurate way. We have focused our analysis on steady optimal control problems characterized by parametric quadratic cost functional constrainedto linear parametric partial differential equations. We have recast them ina saddle-point formulation in order to exploit the consolidated knowledge ofthis kind of structure.A Galerkin-POD algorithm have been applied to several test cases and tosome numerical examples in the field of environmental marine sciences andengineering. Two explicative applications are proposed: a large scale climatologicalapplication and a small scale pollutant control in the Gulf of Trieste. The first one is inserted in forecasting modeling and data assimilation context, the second deals with the safeguard of Gulf of Trieste and surrounding areas.  This work has been carried out in collaboration with OGS (Dr. Renzo Mosetti) as a master thesis in mathematics (SISSA-UniTS) within SISSA mathLab.