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A Refinement-by-Superposition Approach to Fully Anisotropic hp-Refinement for Improved Efficiency in CEM
  • Jeremiah Corrado ,
  • Jake Harmon ,
  • Branislav Notaros
Jeremiah Corrado
Colorado State University

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Jake Harmon
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Branislav Notaros
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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