An Adaptive Anisotropic hp-Refinement Algorithm for the 2D Maxwell Eigenvalue Problem

We present a novel adaptive mesh refinement algorithm for efficiently solving a continuous Galerkin formulation of the 2D Maxwell Eigenvalue Problem over quadrilateral discretizations. The algorithm harnesses a Refinement-by-Superposition framework with support for anisotropic hp-adaptivity. Following a brief summary of the underlying methodology, we develop a novel approach to directing and deploying intelligent fully anisotropic hp-refinements. Numerical examples targeting the Maxwell Eigenvalue problem verify the ability to achieve exponential rates of convergence on a challenging benchmark and demonstrate that including anisotropic refinement yields a significant enhancement of computational efficiency. The success of this algorithm, along with the simplicity of the underlying Refinement-by-Superposition approach, creates a promising path for implementing highly efficient yet lightweight finite element method (FEM) codes for a variety of applications in computational electromagnetics (CEM) and elsewhere.