On the dispersion relation of ADI-FDTD

Garcia, S.G.; Rubio, R.; Bretones, A.R.; Martin, R.G.

doi:10.1109/lmwc.2006.875619

Cited by 30 publications

(21 citation statements)

References 14 publications

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“…However the cut-off frequencies (eigenvalues) differ (sinus functions in FDTD and tangent functions in CN-FDTD), and the numerical dispersion also differs. Similar relative deviations between FDTD and CN-FDTD to the ones commented in the next example for the square waveguide are found (see [9] for more details on the dispersion topic).…”

Section: Resultssupporting

confidence: 81%

“…§ Just for comparison: the non-discrete cut-off frequency is fc = 21.20 GHz while the Yee-FDTD discrete one is 21.11 GHz. The FDTD discrete solution is closer to the non-discrete one, as expected, since the dispersion of CN-FDTD is higher than that of the classical Yee FDTD [9]. This behavior has also been discussed in [28].…”

Section: Resultssupporting

confidence: 74%

“…have received a lot of attraction recently. These approximations suffer up to some extent of numerical errors, which may become severe for some practical applications [8,9].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Efficient Excitation of Waveguides in Crank-Nicolson FDTD

Garcia¹,

Costen²,

Pantoja³

et al. 2010

PIER Letters

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Abstract-In this paper, we present a procedure to calculate the discrete modes propagated with Crank-Nicolson FDTD in metallic waveguides. This procedure enables the correct excitation of this kind of waveguides at any resolution. The problem is reduced to solving an eigenvalue equation, which is performed, both in a closed form, for the usual rectangular waveguide, and numerically in the most general case, validated here with a ridged rectangular waveguide.

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Section: Resultssupporting

confidence: 81%

Section: Resultssupporting

confidence: 74%

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Efficient Excitation of Waveguides in Crank-Nicolson FDTD

Garcia¹,

Costen²,

Pantoja³

et al. 2010

PIER Letters

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“…modes with positive phase velocities) [10]. We note that other perturbations of the Crank-Nicolson FDTD scheme are also of interest for the development of efficient unconditionally stable methods [11].…”

mentioning

confidence: 99%

On Numerical Artifacts of the Complex Envelope ADI-FDTD Method

Jung

Teixeira

Garcia

et al. 2009

IEEE Trans. Antennas Propagat.

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Abstract-We examine two spurious numerical artifacts of the complex envelope (CE) alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method, viz. spurious charges and anomalous wave propagation (modes with positive phase velocity and negative group velocity). These artifacts are also present in the conventional ADI-FDTD; however, the spurious charges in CE-ADI-FDTD have a fundamental distinction from those of ADI-FDTD: they are static in ADI-FDTD and implicitly time-harmonic in CE-ADI-FDTD. Spurious charges are particularly detrimental to CE-ADI-FDTD simulations because they produce secondary radiation. We also show that spurious charges can be reduced by a fixed-point iterative correction in CE-ADI-FDTD.Index Terms-Alternating-direction-implicit finite-difference time-domain (ADI-FDTD), complex envelope (CE), divergence, spurious mode.

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“…Since the solution of the full set of equations for Crank-Nicolson algorithm is far beyond the posibilities of common computing machinery the approximate methods have been developed -the alternatingdirections-implicit (ADI) approach [4][5][6] and the CrankNicolson-split-step (CNSS) approach [7,8]. Character of both these approximations [9] will be shown. Both were in the last decade treated in numerous papers, the interested reader can easily find on himself, and their properties thouroughly investigated.…”

Section: Introductionmentioning

confidence: 99%

On Some Strategies for Computer Simulation of Thewave Propagation Using Finite Differences II. Multi–Dimensional FDTD Method

Sumichrast¹

2013

Journal of Electrical Engineering

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Some strategies used in the computer simulation of wave phenomena by means of finite differences in time-domain (FDTD) method are reviewed and discussed here. It is shown that the wave equation in its discretised form possesses different properties in comparison with the true differential formulation. In this part the issues of stability and numerical dispersion for two-and three-dimensional case of wave propagation in homogeneous space are thoroughly investigated.

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On the dispersion relation of ADI-FDTD

Cited by 30 publications

References 14 publications

Efficient Excitation of Waveguides in Crank-Nicolson FDTD

Efficient Excitation of Waveguides in Crank-Nicolson FDTD

On Numerical Artifacts of the Complex Envelope ADI-FDTD Method

On Some Strategies for Computer Simulation of Thewave Propagation Using Finite Differences II. Multi–Dimensional FDTD Method

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