Explicit structure-preserving discretization of port-Hamiltonian systems with mixed boundary control

In this contribution, port-Hamiltonian systems with non-homogeneous mixed boundary conditions are discretized in a structure-preserving fashion by means of the Partitioned FEM. This means that the power balance and the port-Hamiltonian structure of the continuous equations is preserved at the discrete level. The general construction relies on a weak imposition of the boundary conditions by means of the Hellinger-Reissner variational principle, as recently proposed in Thoma et al., 2021. The case of linear hyperbolic wave-like systems, including the elastodynamic problem and the Maxwell equations in 3D, is then illustrated in detail. A numerical example is worked out on the case of the wave equation.

To cite this paper:
Brugnoli Andrea, Haine Ghislain, Matignon Denis (2022) Explicit structure-preserving discretization of port-Hamiltonian systems with mixed boundary control. IFAC-PapersOnLine 55(30):418–423. Bayreuth, Germany.

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