PDE constrained optimization

In PDE (partial differential equations) constrained optimization arising from structures and vibrations, the objective function requires the evaluation of the output of a large scale dynamical system for a large number of frequencies. This operation is usually expensive to compute. Also, gradients, required by many optimization methods, are expensive to compute. In this research line, we use model order reduction for reducing these costs. Krylov methods are suitable since both the output as the gradients are approximated well near the interpolation points thanks to moment matching. Error estimations on the reduced model are used for a penalty function approach.

The research is conducted in collaboration with the civil engineering department in the framework of the Center of Excellence in Optimization for Engineering (OPTEC). The methods have been applied successfully to optimize the design parameters of dampers for footbridges.