Worked Out Problem 3: Thermal Transfer Problem in a Parametrized Geometry

In this chapter, we consider a scalar elliptic PDE modeling a steady-state heat conduction problem in a two-dimensional and geometrically parametrized holed domain. The aim is to obtain efficient evaluations of the thermal field and the output of interest, defined as the average conduction temperature distribution at the inner walls. 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.