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Proceedings Paper

The nonstandard finite-difference time-domain methodology for broadband calculations
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Paper Abstract

The conventional finite-difference time-domain (FDTD) algorithm, based on 2nd-order finite difference (FD) approximations to the derivatives in Maxwell’s equations, is a simple and flexible methodology that can be used to solve a wide class of problems, but its accuracy is low unless a very fine grid is used. For grid spacing h=Δx=Δy=Δz the error is (epsilon) ~ (h/λ)4 where λ is the wavelength. Putting h → h/2, reduces the error by a factor of 16 but the computation cost rises 16-fold (in three dimensions) because the time step must scale with h to maintain numerical stability. In principle, higher-order FD approximations would improve the accuracy, but they not only complicate the algorithm, but can also render it numerically unstable. We introduced an 8th-order accurate FDTD algorithm with respect to basis function solutions of Maxwell's equations by superposing 2nd-order FDs. This methodology, originally applied to monochromatic propagation, is extended to broadband computations. We validate our methodology on a problem with a known solution.

Paper Details

Date Published: 11 September 2019
PDF: 12 pages
Proc. SPIE 11103, Optical Modeling and System Alignment, 111030O (11 September 2019); doi: 10.1117/12.2529518
Show Author Affiliations
James B. Cole, National Academy of Sciences (United States)
Air Force Institute of Technology (United States)
Saswatee Banerjee, Brillinics Japan, Inc. (Japan)

Published in SPIE Proceedings Vol. 11103:
Optical Modeling and System Alignment
Mark A. Kahan; José Sasián; Richard N. Youngworth, Editor(s)

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