A Skeleton-Based Electromagnetic Recovery for Explicit Adaptive Mesh Refinement

We present a novel adaptive mesh refinement (AMR) algorithm for microwave modeling, specifically focusing on computational electromagnetic analysis using the tangential vector finite element method (TVFEM). For a posteriori error estimation, the proposed explicit recovery-based algorithm uses H(div)-conforming (Brezzi-Douglas-Marini) and H(curl)-conforming (Nedelec) basis functions to recover the artificial electric displacement flux and magnetic vortex density on the mesh skeleton, respectively. Compared with implicit approaches, our approach avoids the need for an auxiliary system with a finer mesh or higher polynomial order. Compared with residual-based approaches, it does not rely on a priori error inequalities, so that it yields a global estimate of the solution quality. Notably, the algorithm aligns mesh topology adjustments with goal-oriented objective functions rather than solely with the numerical solution. Validation is performed using an analytical model with smooth field distribution, a Fichera model with nonsmooth field distribution, a Mie scattering model with a goal-oriented function for monostatic radar cross section (RCS), and a real-world RF filter with a goal-oriented function for insertion loss. Comparative analyses against uniform refinement, nongoal-oriented refinement, and traditional implicit goal-oriented refinement unequivocally demonstrate the superiority of our algorithm.