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

James B. Cole; Saswatee Banerjee

doi:10.1117/12.2529518

11 September 2019 The nonstandard finite-difference time-domain methodology for broadband calculations

James B. Cole, Saswatee Banerjee

Proceedings Volume 11103, Optical Modeling and System Alignment; 111030O (2019) https://doi.org/10.1117/12.2529518
Event: SPIE Optical Engineering + Applications, 2019, San Diego, California, United States

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.

Conference Presentation

Citation Download Citation

James B. Cole and Saswatee Banerjee "The nonstandard finite-difference time-domain methodology for broadband calculations", Proc. SPIE 11103, Optical Modeling and System Alignment, 111030O (11 September 2019); https://doi.org/10.1117/12.2529518

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