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Alternating-direction implicit (ADI) formulation of the finite-difference time-domain (FDTD) method: algorithm and material dispersion implementation

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4 Author(s)
S. W. Staker ; Dept. of Electromagn., MIT, Cambridge, MA, USA ; C. L. Holloway ; A. U. Bhobe ; M. Piket-May

The alternating-direction implicit finite-difference time-domain (ADI-FDTD) technique is an unconditionally stable time-domain numerical scheme, allowing the Δt time step to be increased beyond the Courant-Friedrichs-Lewy limit. Execution time of a simulation is inversely proportional to Δt, and as such, increasing Δt results in a decrease of execution time. The ADI-FDTD technique greatly increases the utility of the FDTD technique for electromagnetic compatibility problems. Once the basics of the ADI-FDTD technique are presented and the differences of the relative accuracy of ADI-FDTD and standard FDTD are discussed, the problems that benefit greatly from ADI-FDTD are described. A discussion is given on the true time savings of applying the ADI-FDTD technique. The feasibility of using higher order spatial and temporal techniques with ADI-FDTD is presented. The incorporation of frequency dependent material properties (material dispersion) into ADI-FDTD is also presented. The material dispersion scheme is implemented into a one-dimensional and three-dimensional problem space. The scheme is shown to be both accurate and unconditionally stable.

Published in:

IEEE Transactions on Electromagnetic Compatibility  (Volume:45 ,  Issue: 2 )