A Refinement-by-Superposition Approach to Fully Anisotropic
hp-Refinement for Improved Efficiency in CEM
Abstract
We present an application of fully anisotropic hp-adaptivity over
quadrilateral meshes for H(curl)-conforming discretizations in
Computational Electromagnetics (CEM). Traditionally, anisotropic
h-adaptivity has been difficult to implement under the constraints of
the Continuous Galerkin Formulation; however,
Refinement-by-Superposition (RBS) facilitates anisotropic mesh
adaptivity with great ease. We present a general discussion of the
theoretical considerations involved with implementing fully anisotropic
hp-refinement, as well as an in-depth discussion of the practical
considerations for 2-D FEM. Moreover, to demonstrate the benefits of
both anisotropic h- and p-refinement, we study the 2-D Maxwell
eigenvalue problem as a test case. The numerical results indicate that
fully anisotropic refinement can provide significant gains in
efficiency, even in the presence of singular behavior, substantially
reducing the number of degrees of freedom required for the same accuracy
with isotropic hp-refinement. This serves to bolster the relevance of
RBS and full hp-adaptivity to a wide array of academic and industrial
applications in CEM