A high order mixed vector finite element method for solving the time dependent Maxwell equations on unstructured grids

  • Authors:

  • R. N. Rieben;G. H. Rodrigue;D. A. White

  • Affiliations:

  • Defense Sciences Engineering Division, Lawrence Livermore National Laboratory, P.O. Box 808 - L419, Livermore, CA 94551, USA;University of California at Davis, Department of Applied Science, Davis, CA, USA and Lawrence Livermore National Laboratory, Institute for Scientific Computing Research, P.O. Box 808 - L227, Liver ...;Defense Sciences Engineering Division, Lawrence Livermore National Laboratory, P.O. Box 808 - L419, Livermore, CA 94551, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2005

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Abstract

We present a mixed vector finite element method for solving the time dependent coupled Ampere and Faraday laws of Maxwell's equations on unstructured hexahedral grids that employs high order discretization in both space and time. The method is of arbitrary order accuracy in space and up to 4th order accurate in time, making it well suited for electrically large problems where grid anisotropy and numerical dispersion have plagued other methods. In addition, the method correctly models both the jump discontinuities and the divergence-free properties of the electric and magnetic fields, is charge and energy conserving, conditionally stable, and free of spurious modes. Several computational experiments are performed to demonstrate the accuracy, efficiency and benefits of the method.