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The Alternating Direction Implicit (ADI) Formulation of the Finite-Difference Time-Domain (FDTD) Method: Algorithm and Material Dispersion Implementation

Published

Author(s)

Shawn W. Staker, Christopher L. Holloway, Alpesh Bhobe, Melinda Piket-May, Tobin A. Driscoll

Abstract

The ADI-FDTD technique is an unconditionally stable time-domain numerical scheme, allowing the Δ}t time step to be increased beyond the Courant-Friedrichs-Lewy (CFL) limit. Execution time of a simulation is inversely proportional to Δ}t, and as such increasing Δ}t results in a decrease of execution time. The ADI-FDTD technique greatly increases the utility of the FDTD technique for EMC problems. Once the basics of the ADI-FDTD technique are presented, a discussion on the relative accuracy of ADI-FDTD as compared to standard FDTD is presented. The identification of problems which greatly benefit from ADI-FDTD are described. These problems are referred to as ADI class problems. An empirical formula is presented which estimates 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 material dispersion into ADI-FDTD is also presented. The material dispersion scheme is implemented into a one and three dimensional problem space. The scheme is shown to be unconditionally stable, and to possess an accuracy level enabling it to be applicable to ADI class problems.
Citation
IEEE Trans EMC: Special Issue on Advanced EMC Numerical Modeling
Volume
45
Issue
2

Keywords

ADI-FDTD, FDTD, higher order schemes, material dispersion, unconditionally stable, ADI

Citation

Staker, S. , Holloway, C. , Bhobe, A. , Piket-May, M. and Driscoll, T. (2003), The Alternating Direction Implicit (ADI) Formulation of the Finite-Difference Time-Domain (FDTD) Method: Algorithm and Material Dispersion Implementation, IEEE Trans EMC: Special Issue on Advanced EMC Numerical Modeling (Accessed April 19, 2024)
Created April 30, 2003, Updated October 12, 2021