Adaptive hp-Refinement for 2-D Maxwell Eigenvalue Problems: Method and Benchmarks

We present an application of goal-oriented adaptive isotropic hp-refinement for the 2-D Maxwell eigenvalue problem. We apply a simplified goal-oriented error expression for improving the accuracy of the eigenvalues, which, when combined with indicators derived from the solution, enables highly targeted discretization tuning. Furthermore, we introduce an hp-refinement/coarsening optimizer coupled with smoothness estimation for refinement classification and execution. These enhancements yield cost-effective resource allocations that reach extremely high accuracy rapidly even for eigenvalues of singular eigenfunctions. Finally, we provide numerical benchmarks more accurate than existing numerical reference values, along with new benchmarks for higher order modes that will facilitate the comparison and development of new approaches to adaptivity and hp finite elements in computational electromagnetics (CEM). Our implementation is based on the open-source finite element library deal.II.