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Metallic rectangular waveguides are often the preferred choice on telecommunication systems and medical equipment working on the upper microwave and millimeter wave frequency bands due to the simplicity of its geometry, low losses, and the capacity to handle high powers. Waveguide translational symmetry is interrupted by the unavoidable presence of bends, transitions, and junctions, among others. This paper employs a 3D hp self-adaptive grid-refinement finite element strategy for the solution of these relevant electromagnetic waveguide problems. These structures often incorporate dielectrics, metallic screws, round corners, and so on, which may facilitate its construction or improve its design, but significantly difficult its modeling when employing semi-analytical techniques. The hp-adaptive finite element method enables accurate modeling of these structures even in the presence of complex materials and geometries. Numerical results demonstrate the suitability of the hp-adaptive method for modeling these waveguide structures, delivering errors below 0.5% with a limited number of unknowns. Solutions of waveguide problems obtained with the self-adaptive hp-FEM are of comparable accuracy to those obtained with semi-analytical techniques such as the Mode Matching method, for problems where the latest methods can be applied. At the same time, the hp-adaptive FEM enables accurate modeling of more complex waveguide structures.
finite element method (fem) ; hp-adaptivity; electromagnetic waveguides