A Refinement-by-Superposition hp-Method for H(curl)- and H(div)-Conforming Discretizations

We present an application of refinement-by-superposition (RBS) hp-refinement in computational electromagnetics (CEM), which permits exponential rates of convergence. In contrast to dominant approaches to hp-refinement for continuous Galerkin methods, which rely on constrained-nodes, the multi-level strategy presented drastically reduces the implementation complexity. Through the RBS methodology, enforcement of continuity occurs by construction, enabling arbitrary levels of refinement with ease and without the practical (but not theoretical) limitations of constrained-node refinement. We outline the construction of the RBS hp-method for refinement with H(curl)- and H(div)-conforming finite cells. Numerical simulations for the 2-D finite element method (FEM) solution of the Maxwell eigenvalue problem demonstrate the effectiveness of RBS hp-refinement. An additional goal of this work, we aim to promote the use of mixed-order (low- and high-order) elements in practical CEM applications.