Open Access

ARTICLE

A Discrete Differential Forms Framework for Computational Electromagnetism

P. Castillo², J. Koning³, R. Rieben⁴, D. White⁵
1 This work was performed under the auspices of the U.S. Department of Energy by the University of California, Lawrence Livermore National Laboratory
2 Department of Mathematics, University of Puerto Rico castillo@math.uprm.edu
3Defense Sciences Engineering Division, Lawrence Livermore National Laboratory, koning1@llnl.gov
4University of California, Davis and Institute for Scientific Computing Research, Lawrence Livermore National Laboratory, rieben1@llnl.gov
5Defense Sciences Engineering Division, Lawrence Livermore National Laboratory, white37@llnl.gov

Computer Modeling in Engineering & Sciences 2004, 5(4), 331-346. https://doi.org/10.3970/cmes.2004.005.331

Abstract

In this article, we present a computational framework for solving problems arising in electromagnetism. The framework is derived from a modern geometrical approach and is based on differential forms (or p-forms). These geometrical entities provide a natural framework for modeling of physical quantities such as electric potentials, electric and magnetic fields, electric and magnetic fluxes, etc. We have implemented an object oriented class library, called FEMSTER. The library is designed for high order finite element approximations. In addition, it can be expanded by including user-defined data types or by deriving new classes. Finally, the versatility of the software is shown through different simulations.

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Keywords

High order finite element, H(div) and H(curl) - conforming methods, Computational electromagnetism, Object oriented programming.

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