Modelling and structure-preserving discretization of Maxwell’s equations as port-Hamiltonian system

Gabriel Payen (1) , Denis Matignon (1) , Ghislain Haine (1)

1 DISC - Département d'Ingénierie des Systèmes Complexes

The modelling and discretization of the boundary controlled 3D Maxwell’s equations as a port-Hamiltonian system is addressed. The proposed scheme, based on the Partitioned Finite Element Method (PFEM), originally proposed in Cardoso-Ribeiro et al. (2018), preserves the Dirac structure at the discrete level. Two types of damping phenomena are taken into account: Joule’s effect, and a matrix-valued impedance at the boundary, both being preserved by PFEM, as presented in Serhani et al. (2019a).

Mots clés: Maxwell’s equations; Port-Hamiltonian system; Partitioned Finite Element Method; Dirac structure; Impedance; Boundary control and observation

Domaines: Réseaux et télécommunications [cs.NI]

Gabriel Payen, Denis Matignon, Ghislain Haine. Modelling and structure-preserving discretization of Maxwell’s equations as port-Hamiltonian system. The 21th World Congress of The International Federation of Automatic Control (IFAC 2020), Jul 2020, Berlin (virtual), Germany. pp.7581-7586, ⟨10.1016/j.ifacol.2020.12.1355⟩. ⟨hal-03208702⟩