Performance evaluation of several implicit FDTD methods for optical waveguide analyses

Shibayama, Jun; Muraki, Masatake; Takahashi, Ryo; Yamauchi, Junji; Nakano, Hisamatsu

doi:10.1109/jlt.2006.874570

Cited by 51 publications

(26 citation statements)

References 34 publications

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“…7. We note again that the observed accuracy of LOD-FDTD is poorer than that of ADI-FDTD in this case, differently from other examples [24], [29], [30]. Fig.…”

Section: B Relative Accuracymentioning

confidence: 51%

See 1 more Smart Citation

A Study on Unconditionally Stable FDTD Methods for the Modeling of Metamaterials

Nascimento¹,

Jung

Borges

et al. 2009

J. Lightwave Technol.

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“…7. We note again that the observed accuracy of LOD-FDTD is poorer than that of ADI-FDTD in this case, differently from other examples [24], [29], [30]. Fig.…”

Section: B Relative Accuracymentioning

confidence: 51%

“…The relative performance of various unconditionally stable FDTD methods was recently evaluated, e.g., consisting of positive-index media only [30]. In the present study, we evaluate unconditionally stable FDTD methods in more challenging problems including negative-index media.…”

mentioning

confidence: 99%

A Study on Unconditionally Stable FDTD Methods for the Modeling of Metamaterials

Nascimento¹,

Jung

Borges

et al. 2009

J. Lightwave Technol.

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show abstract

“…Compared with the 3-D FDTD and ADI-BOR-FDTD result, they show good agreement and at least 80% of computational time to the ADI counterparts. Nakano, 2006), the numerical results is comparable to the ADI counterparts which has second-order accurate in time. Although the locally 1-D (LOD)-BOR-FDTD is developed, but no dispersive media was considered.…”

Section: Introductionmentioning

confidence: 54%

LOD-BOR-FDTD Algorithm for Analyzing Debye Dispersive Media by Bilinear Z Transforms

Pin¹

2011

MAS

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In order to reduce memory usage and improve efficiency, the unconditionally stable locally 1-D (LOD)-FDTD method for bodies of revolution (BOR) is extended to Debye dispersive media based on the bilinear Z transform (BZT) theory. The LOD-BOR-FDTD method is proposed. To validate the Higher efficiency and Lower memory usage of the proposed algorithm, two numerical examples are given. Compared with the 3-D FDTD and ADI-BOR-FDTD result, they show good agreement and at least 80% of computational time to the ADI counterparts. Nakano, 2006), the numerical results is comparable to the ADI counterparts which has second-order accurate in time. Although the locally 1-D (LOD)-BOR-FDTD is developed, but no dispersive media was considered. On the other hand, the use of Z transforms (D. M. Sullivan, 1992) to the treatment of dispersive media in FDTD is an attractive alternative, since it has the advantage that the complicated convolution integrals can simply be reduced to algebraic equations, and the relationship between the flux density and the electric field can readily be translated into finite-difference equations. But we found the conventional Z transforms could bring higher error for Dispersive Media. So the bilinear Z transforms (BZT) is used to avoid error for the trapezoidal integration is more accurate than rectangular integration (D. M. Sullivan, 2000). This fact motivates us to apply the bilinear Z transforms to the LOD-BOR-FDTD for a concise frequency-dependent formulation. In this letter, we use the BZT method to build an extension of the LOD-BOR-FDTD to Debye dispersive media in order to reduce memory usage and improve efficiency. Formulation Bilinear Z TransformsFor Debye dispersive medium having p poles, the electric flux density D and the electric field E in the frequency domain are related as (A. Taflove and S. C. Hagness, 2005)

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“…Examples of these implicit methods are Crank-Nicolson (CN) FDTD [9], alternating direction implicit (ADI) FDTD [10], locally one-dimensional (LOD) FDTD [11,12] and Laguerre-FDTD [13,14]. A lot of comparisons concerning the CPU-time and accuracy of these implicit schemes have been reported [15]- [17]. Compared to explicit methods, they all reduce the number of time steps per simulation at the expense of a higher computational effort per time step.…”

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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Performance evaluation of several implicit FDTD methods for optical waveguide analyses

Cited by 51 publications

References 34 publications

A Study on Unconditionally Stable FDTD Methods for the Modeling of Metamaterials

A Study on Unconditionally Stable FDTD Methods for the Modeling of Metamaterials

LOD-BOR-FDTD Algorithm for Analyzing Debye Dispersive Media by Bilinear Z Transforms

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

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