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Energy-Norm-Based and Goal-Oriented Automatic hp Adaptivity for Electromagnetics: Application to Waveguide Discontinuities

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3 Author(s)
Garcia-Castillo, L.E. ; Escuela Politec. Super., Dept. de Teor. de la Serial y Commun., Univ. Carlos III de Madrid, Leganes ; Pardo, D. ; Demkowicz, L.F.

The finite-element method (FEM) enables the use of ldquoadaptedrdquo meshes. The simultaneous combination of h (local variations in element size) and p (local variations in the polynomial order of approximation) refinements, i.e., hp-adaptivity, is the most powerful and flexible type of adaptivity. In this paper, two versions of a fully automatic hp-adaptive FEM for electromagnetics are presented. The first version is based on minimizing the energy-norm of the error. The second, namely the goal oriented strategy, is based on minimizing the error of a given (user-prescribed) quantity of interest. 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 2-D analysis of H -plane rectangular waveguide discontinuities. Stabilized variational formulations and H(curl) FEM discretizations in terms of quadrilaterals of variable order of approximation supporting anisotropy and hanging nodes are used. Comparison of energy-norm and goal-oriented hp-adaptive strategies in the context of waveguiding problems is provided. Specifically, the scattering parameters of the discontinuity are used as goal.

Published in:

Microwave Theory and Techniques, IEEE Transactions on  (Volume:56 ,  Issue: 12 )