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

S. J. Cooke, M. Botton, T. M. Antonsen, B. Levush

Research output: Contribution to journalArticlepeer-review

92 Scopus citations


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.

Original languageAmerican English
Pages (from-to)187-200
Number of pages14
JournalInternational Journal of Numerical Modelling: Electronic Networks, Devices and Fields
Issue number2
StatePublished - Mar 2009
Externally publishedYes


  • Electromagnetic propagation
  • FDTD methods
  • Simulation


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