A leapfrog formulation of the 3-D ADI-FDTD algorithm

  • Authors:

  • S. J. Cooke;M. Botton;T. M. Antonsen, Jr.;B. Levush

  • Affiliations:

  • Naval Research Laboratory, Washington, DC 20375, U.S.A.;University of Maryland, College Park, MD 20742, U.S.A.;University of Maryland, College Park, MD 20742, U.S.A.;Naval Research Laboratory, Washington, DC 20375, U.S.A.

  • Venue:
  • International Journal of Numerical Modelling: Electronic Networks, Devices and Fields - Focussed Issue on the Seventh International Workshop on Computational Electromagnetics in the Time-Domain (CEM-TD)
  • Year:
  • 2009

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Abstract

We introduce a new, alternative form of the 3-D alternating direction implicit finite-difference time-domain (ADI-FDTD) algorithm that has a number of attractive properties for electromagnetic simulation. We obtain a leapfrog form of the time-advance equations, where the E and H fields are staggered at half-integer and integer time steps, respectively, that preserves the unconditional stability of the ADI-FDTD method. The resulting equations resemble the explicit leapfrog-FDTD method, but the field update equations are modified to include the solution of sets of tri-diagonal equations at each step, similar to the original ADI-FDTD scheme, so that the scheme is not constrained by the Courant–Friedrichs–Lewy limit. The algorithm is simpler than the ADI-FDTD method but algebraically equivalent, allowing a reduction in computation to achieve the same numerical solution. We discuss the advantages of the formulation over the original FDTD and ADI-FDTD methods, and confirm our results numerically. Published in 2008 by John Wiley & Sons, Ltd. This article is a U.S. Government work and is in the public domain in the U.S.A.