Fully Automatic hp Adaptivity for Electromagnetics, Application to the Analysis of H-Plane and E-Plane Rectangular Waveguide Discontinuities

Within the finite element method, the hp-adaptivity, i.e., the simultaneous combination of the h (local variations in element size) and p (local variations in the polynomial order of approximation) adaptivities, is the most powerful and flexible type of adaptivity. In this paper, a fully automatic hp-adaptive finite element method for electromagnetics is presented. The adaptive strategy delivers exponential convergence rates for the error even in the presence of singularities. The hp adaptivity is presented in the context of the two dimensional problem consisting in the analysis of H-plane and E-plane rectangular waveguide discontinuities. Stabilized variational formulations and H(curl) FEM discretizations in terms of quadrangles of variable order of approximation supporting anisotropy and hanging nodes are used. A wide variety of structures have been analyzed, and their scattering parameters computed. Results for two structures are presented.