In this contribution, we extend the hybridization framework for the Hodge Laplacian [Awanou et al., Hybridization and postprocessing in finite element exterior calculus, 2023] 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. This scheme is equivalent to the second order mixed Galerkin formulation and retains a discrete power balance and discrete conservation laws. The mixed formulation is also equivalent to the hybrid formulation. The discretization can be reinterpreted as a power preserving interconnection of port-Hamiltonian systems, thus providing a system theoretic interpretation of finite element assembly. The hybrid system can be 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 one field is completely discarded. Numerical experiments on the 3D wave and Maxwell equations show the convergence of the method and the size reduction achieved by the hybridization.

翻译：本文中，我们将霍奇拉普拉斯算子的混合化框架[Awanou等人，有限元外微积分中的混合化与后处理，2023]扩展至描述线性波传播现象的端口-哈密顿系统。为此，我们引入一种双场混合伽辽金离散格式，其中一个变量通过协调有限元空间逼近，而第二个变量则完全局部化。该格式等价于二阶混合伽辽金公式，并保留了离散功率平衡与离散守恒律。混合公式也等价于混合化公式。该离散化可重新解释为端口-哈密顿系统的功率保持互联，从而为有限元组装提供系统理论解释。混合化系统可通过离散时间静态凝聚过程高效求解。与霍奇拉普拉斯算子相比，由于其中一个场被完全舍弃，混合化所实现的规模缩减更大。三维波动方程与麦克斯韦方程的数值实验验证了该方法的收敛性以及混合化实现的规模缩减效果。