Worked Out Problem 8: A Nonlinear Parabolic FitzHugh–Nagumo Problem

In this chapter, we consider a vector nonlinear parabolic PDE modeling the unsteady FitzHugh–Nagumo system in a one-dimensional domain. The aim is to obtain efficient evaluations of the unknown fields describing the voltage and the recovery voltage. 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 and the speedup. We provide the links to the source code, to the Jupyter notebook, and to the web-server ARGOS.