Worked Out Problem 16: A Parametrized Elliptic Optimal Control Problem

In this chapter, we consider a linear-quadratic optimal control problem with a vector elliptic PDE constraint in a two-dimensional and geometrically parametrized domain. The aim is to obtain efficient evaluations of the optimal temperature distribution, the adjoint, the optimal control field and the output of interest, defined as the cost functional. The solution is approximated using reduced order modeling techniques based on the POD-Galerkin method. The problem is described by presenting the physical domain, the goal, the parametrization, the boundary conditions, the governing PDE, and the corresponding weak formulation with its affine decomposition. Numerical results show the performance of the reduced approach with respect to the high-fidelity discretization, the quantity of interest, and the speedup. We provide the links to the source code, to the Jupyter notebook, and to the web-server ARGOS.