Numerical investigation of a 3D hybrid high-order method for the indefinite time-harmonic Maxwell problem

Abstract

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 $hp$-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 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.