A more accurate, stable, FDTD algorithm for electromagnetics in anisotropic dielectrics

A more accurate, stable, finite-difference time-domain (FDTD) algorithm is developed for simulating Maxwellʼs equations with isotropic or anisotropic dielectric materials. This algorithm is in many cases more accurate than previous algorithms (G.R. Werner et al., 2007 [5]; A.F. Oskooi et al., 2009 [...

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Bibliographic Details
Published in:Journal of computational physics 2013-12, Vol.255, p.436-455
Main Authors: Werner, Gregory R., Bauer, Carl A., Cary, John R.
Format: Article
Language:English
Subjects:
Algorithms
Anisotropic
Anisotropy
Dielectric
Dielectrics
Discontinuity
Electromagnetic
Embedded boundary
Errors
FDTD
Finite difference time domain method
Mathematical analysis
Maxwell
Remedies
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Summary:A more accurate, stable, finite-difference time-domain (FDTD) algorithm is developed for simulating Maxwellʼs equations with isotropic or anisotropic dielectric materials. This algorithm is in many cases more accurate than previous algorithms (G.R. Werner et al., 2007 [5]; A.F. Oskooi et al., 2009 [7]), and it remedies a defect that causes instability with high dielectric contrast (usually for ϵ≫10) with either isotropic or anisotropic dielectrics. Ultimately this algorithm has first-order error (in the grid cell size) when the dielectric boundaries are sharp, due to field discontinuities at the dielectric interface. Accurate treatment of the discontinuities, in the limit of infinite wavelength, leads to an asymmetric, unstable update (C.A. Bauer et. al., 2011 [6]), but the symmetrized version of the latter is stable and more accurate than other FDTD methods. The convergence of field values supports the hypothesis that global first-order error can be achieved by second-order error in bulk material with zero-order error on the surface. This latter point is extremely important for any applications measuring surface fields.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2013.08.009