Dual field structure-preserving discretization of port-Hamiltonian systems using finite element exterior calculus

In this paper we propose a novel approach to discretize linear port-Hamiltonian systems while preserving the underlying structure. We present finite element exterior calculus formulation that is able mimetically represent conservation laws and cope with mixed open boundary conditions using single computational mesh. The possibility of including allows for modular composition complex multi-physical whereas provides coordinate-free treatment. Our relies on dual-field representation physical system redundant at continuous level but eliminates need mimicking Hodge star operator discrete level. By considering Stokes-Dirac structure representing together its adjoint, which embeds metric information directly in codifferential, an explicit avoided altogether. imposing strong manner, power balance characterizing then retrieved via symplectic Runge-Kutta integrators based Gauss-Legendre collocation points. Numerical experiments validate convergence method properties terms energy both wave Maxwell equations three dimensional domain. For latter example, magnetic electric fields preserve their divergence free nature