Reduced basis methods for optimal control of advection-diffusion problems

MOX 79

Reduced basis methods for optimal control of advection-diffusion problems

Monday 30th January 2006

Quarteroni, Alfio; Rozza, Gianluigi; Quaini, Annalisa

The reduced basis (RB) method is proposed for the approximation of multiparametrized equations governing an optimal control problem. The idea behind the RB method is to project the solution onto a space of small dimension, specifically designed on the problem at hand, and to decouple the generation and projection stages (off-line/on-line computational procedures) of the approximation process in order to solve parametrized equations in a rapid and not expensive way. The application that we investigate is an air pollution control problem: we aim at regulating the emissions of industrial chimneys in order to keep the pollutant concentration below a certain threshold over an observation area, like a town. Adopting the RB method for both state and adjoint equations of the optimal control problem leads to important computational savings with respect to the use of the Galerkin-finite element method. We consider different parametrization (control, physical and geometrical input parameters) so that we are able to solve the control problem from a global and decisional point of view.