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A leapfrog formulation of the 3‐D ADI‐FDTD algorithm
Author(s) -
Cooke S. J.,
Botton M.,
Antonsen T. M.,
Levush B.
Publication year - 2008
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/jnm.707
Subject(s) - finite difference time domain method , mathematics , integer (computer science) , alternating direction implicit method , diagonal , algorithm , stability (learning theory) , field (mathematics) , computation , finite difference method , computer science , mathematical analysis , pure mathematics , geometry , physics , quantum mechanics , machine learning , programming language
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.