Hybrid High-Order (HHO) methods are a recently developed class of methods belonging to the broader family of Discontinuous Sketetal methods. Other well known members of the same family are the well-established Hybridizable Discontinuous Galerkin (HDG) method, the nonconforming Virtual Element Method (ncVEM) and the Weak Galerkin (WG) method. HHO provides various valuable assets such as simple construction, support for fully-polyhedral meshes and arbitrary polynomial order, great computational efficiency, physical accuracy and straightforward support for -refinement. In this work we propose an HHO method for the indefinite time-harmonic Maxwell problem and we evaluate its numerical performance. In addition, we present the validation of the method in two different settings: a resonant cavity with Dirichlet conditions and a parallel plate waveguide problem with a total/scattered field decomposition and a plane-wave boundary condition. Finally, as a realistic application, we demonstrate HHO used on the study of the return loss in a waveguide mode converter.

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不定时谐麦克斯韦问题的 3D 混合高阶方法的数值研究

混合高阶 (HHO) 方法是最近开发的一类方法，属于更广泛的不连续骨架方法家族。同一家族的其他著名成员包括完善的可杂交不连续伽辽金 (HDG) 方法、非相容虚拟单元方法 (ncVEM) 和弱伽辽金 (WG) 方法。HHO 提供了各种有价值的资产，例如简单的构造、对全多面体网格和任意多项式阶次的支持、出色的计算效率、物理准确性和对细化的直接支持。在这项工作中，我们提出了一种用于不定时谐麦克斯韦问题的 HHO 方法，并评估了其数值性能。此外，我们在两种不同的设置下对该方法进行了验证：具有狄利克雷条件的谐振腔和具有总/散射场分解和平面波边界条件的平行板波导问题。最后，作为一个实际应用，我们演示了 HHO 用于研究波导模式转换器的回波损耗。