Implicit Local Refinement for Evanescent Layers Combined With Classical FDTD

Tierens, W.; Zutter, D. De

doi:10.1109/lmwc.2013.2253090

Cited by 4 publications

(2 citation statements)

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“…The HIE scheme leverages some ideas reported in [23]- [25], where a fully collocated and unconditionally stable implicit method to simulate electromagnetic waves in fusion plasmas was presented. In [24], this fully collocated implicit method is combined with classical FDTD to obtain a 1D local refinement scheme. The HIE-FDTD method described here is the extension of this preliminary work to two dimensions.…”

Section: Introductionmentioning

confidence: 99%

A New Hybrid Implicit–Explicit FDTD Method for Local Subgridding in Multiscale 2-D TE Scattering Problems

Londersele

Zutter

Ginste

2016

IEEE Trans. Antennas Propagat.

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Abstract-The conventional Finite-Difference Time-Domain (FDTD) method with staggered Yee scheme does not easily allow including thin material layers, especially so if these layers are highly conductive. This paper proposes a novel subgridding technique for 2D problems, based on a Hybrid Implicit-Explicit (HIE) scheme, that efficiently copes with this problem. In the subgrid, the new method collocates field components such that the thin layer boundaries are defined unambiguously. Moreover, aspect ratios of more than a million do not impair the stability of the method and allow for very accurate predictions of the skin effect. The new method retains the Courant limit of the coarse Yee grid and is easily incorporated into existing FDTD codes. A number of illustrative examples, including scattering by a metal grating, demonstrate the accuracy and stability of the new method.

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Section: Introductionmentioning

confidence: 99%

A New Hybrid Implicit–Explicit FDTD Method for Local Subgridding in Multiscale 2-D TE Scattering Problems

Londersele

Zutter

Ginste

2016

IEEE Trans. Antennas Propagat.

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“…This stability criterion can be restrictive, as it forces us to choose a small ∆ t and thus to run a very large number of time steps to simulate a given length of time. This is especially so when the phenomena of interest are waves that move much slower than c, but the time step still needs to be chosen based on c [16], when small features, much smaller than the wavelength, need to be resolved [17,2,3,8], or when the simulation region has an extreme aspect ratio [18].…”

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confidence: 99%

Unification of Leapfrog and Crank--Nicolson Finite Difference Time Domain Methods

Tierens

2018

SIAM J. Sci. Comput.

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In this paper we present a unified theory of explicit (leapfrog) and implicit (Crank-Nicolson) FDTD time-stepping schemes. This enables us to interface leapfrog FDTD with Crank-Nicolson FDTD and we will prove that the result is stable at the Courant limit of the leapfrog part. It also enables us to construct explicit FDTD-like algorithms whose stability condition is less restrictive than that of leapfrog FDTD, and a remarkable explicit 1:2 FDTD refinement scheme which is stable up to the Courant limit of the coarse part.

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