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Modular hp-FEM system HERMES and its application to Maxwell’s equations

Author

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  • Vejchodský, Tomáš
  • Šolín, Pavel
  • Zítka, Martin

Abstract

In this paper, we introduce a multi-physics modular hp-FEM system HERMES. The code is based on a novel approach where the finite element technology (mesh processing and adaptation, numerical quadrature, assembling and solution of the discrete problems, a-posteriori error estimation, etc.) is fully separated from the physics of the solved problems. The physics is represented via simple modules containing PDE-dependent parameters as well as hierarchic higher-order finite elements satisfying the conformity requirements imposed by the PDE. After describing briefly the modular structure of HERMES and some of its functionality, we focus on its application to the time-harmonic Maxwell’s equations. We present numerical results which illustrate the capability of the hp-FEM to reduce both the number of degrees of freedom and the CPU time dramatically compared to standard lowest-order FEM.

Suggested Citation

  • Vejchodský, Tomáš & Šolín, Pavel & Zítka, Martin, 2007. "Modular hp-FEM system HERMES and its application to Maxwell’s equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 76(1), pages 223-228.
    • Handle: RePEc:eee:matcom:v:76:y:2007:i:1:p:223-228
    DOI: 10.1016/j.matcom.2007.02.001
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    Cited by:

    1. Šolín, Pavel & Červený, Jakub & Doležel, Ivo, 2008. "Arbitrary-level hanging nodes and automatic adaptivity in the hp-FEM," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(1), pages 117-132.

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