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We consider the design of structure-preserving discretization methods for thesolution of systems of boundary controlled Partial Differential Equations(PDEs) thanks to the port-Hamiltonian formalism. We first provide a novelgeneral structure of infinite-dimensional port-Hamiltonian systems (pHs) forwhich the Partitioned Finite Element Method (PFEM) straightforwardly applies.The proposed strategy is applied to abstract multidimensional linear hyperbolicand parabolic systems of PDEs. Then we show that instructional model problemsbased on the wave equation, Mindlin equation and heat equation fit within thisunified framework. Secondly we introduce the ongoing project SCRIMP (Simulationand ContRol of Interactions in Multi-Physics) developed for the numericalsimulation of infinite-dimensional pHs. SCRIMP notably relies on the FEniCSopen-source computing platform for the finite element spatial discretization.Finally, we illustrate how to solve the considered model problems within thisframework by carefully explaining the methodology. As additional support,companion interactive Jupyter notebooks are available.

Numerical approximation of port-Hamiltonian systems for hyperbolic or parabolic PDEs with boundary control