Numerical investigation of a 3D Hybrid High-Order Method for the Indefinite Time-Harmonic Maxwell Problem

Overview & Synopsis

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 wellestablished Hybridizable Discontinuous Galerkin (HDG) method 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 hp-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 only Dirichlet conditions and a parallel plate waveguide problem employing all the available boundary conditions. Finally, as a realistic application, we demonstrate HHO used on the study of the return loss in a waveguide mode converter.