Finite element hybridization of port-Hamiltonian systems

Abstract

In this contribution, we extend the hybridization framework for the Hodge Laplacian [Awanou et al. (2023) [16]] to port-Hamiltonian systems describing linear wave propagation phenomena. To this aim, a dual field mixed Galerkin discretization is introduced, in which one variable is approximated via conforming finite element spaces, whereas the second is completely local. The mixed formulation is then hybridized to obtain an equivalent formulation that can be more efficiently solved using a static condensation procedure in discrete time. The size reduction achieved thanks to the hybridization is greater than the one obtained for the Hodge Laplacian as the final system only contains the globally coupled traces of one variable. Numerical experiments on the 3D wave and Maxwell equations illustrate the convergence of the method and the size reduction achieved by the hybridization.