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

Authors:
Tomáš Vejchodský;Pavel Šolín;Martin Zítka
Affiliations:
Mathematical Institute, Academy of Sciences, itná 25, 11567 Praha 1, Czech Republic;Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968-0514, USA;Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968-0514, USA
Venue:
Mathematics and Computers in Simulation
Year:
2007

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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.