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 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：本文扩展了Hodge Laplacian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]，将其应用于描述线性波传播现象的端口-哈密顿系统。为此，我们引入了一种对偶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近似，而另一个变量则完全局域化。该格式等价于二阶混合伽辽金公式，并保持了离散功率平衡与离散守恒律。混合公式与混合化公式也等价。混合系统可通过离散时间中的静态凝聚过程高效求解。由于其中一个场被完全消去，混合化带来的规模缩减效果优于Hodge Laplacian。针对三维波动方程和麦克斯韦方程的数值实验验证了方法的收敛性及混合化实现的规模缩减效果。