Some unconditionally stable time stepping methods for the 3D Maxwell's equations

  • Authors:

  • Jongwoo Lee;Bengt Fornberg

  • Affiliations:

  • Department of Mathematics, Kwangwoon University, 447-1 Wolgye-Dong, Nowon-Gu, Seoul 139-701, South Korea;Department of Applied Mathematics, University of Colorado, 526 UCB, Boulder, CO

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2004

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Abstract

Almost all the difficulties that arise in the numerical solution of Maxwell's equations are due to material interfaces. In case that their geometrical features are much smaller than a typical wavelength, one would like to use small space steps with large time steps. The first time stepping method which combines a very low cost per time step with unconditional stability was the ADI-FDTD method introduced in 1999. The present discussion starts with this method, and with an even more recent Crank-Nicolson-based split step method with similar properties. We then explore how these methods can be made even more efficient by combining them with techniques that increase their temporal accuracies.