Worked Out Problem 5: Heat Conduction with Gaussian Flux

In this chapter, we consider a scalar elliptic PDE modeling the steady heat conduction problem with a non-affine Gaussian flux in a two-dimensional domain. The aim is to obtain efficient evaluations of the thermal field and the output of interest, defined as the integral of the source term. The solution is approximated using reduced order modeling techniques based on the Greedy algorithm and the Empirical Interpolation 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.