Higher order absorbing boundary conditions for the finite-difference time-domain method

Tirkas, P.A.; Balanis, C.A.; Renaut, Rosemary A.

doi:10.1109/8.182454

Cited by 56 publications

(14 citation statements)

References 9 publications

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“…Figures 2 and 3 show the local and the global errors, as defined in [8], for lossless FDTD domain. The local error is for the PML/computational domain interface at y ϭ Ϫ25⌬ as observed at time 100⌬t.…”

Section: Numerical Studymentioning

confidence: 99%

“…A point source excites a 100⌬ ϫ 50⌬ isotropic homogeneous computational domain at its center with ⌬t ϭ 25ps and ⌬ ϭ ⌬x ϭ ⌬y ϭ 2c⌬t. The excitation pulse used is the derivative of the pulse used in [8]. This pulse was preferred, as it has low numerical grid dispersion [9].…”

Section: Numerical Studymentioning

confidence: 99%

“…The computational domain was terminated by eight PML layers with a quadratic conductivity profile and a maximum theoretical reflection coefficient of 10 Ϫ5 at normal incidence, expressed as PML [8,2,0.001] in Berenger's notation [4]. Figures 2 and 3 show the local and the global errors, as defined in [8], for lossless FDTD domain.…”

Section: Numerical Studymentioning

confidence: 99%

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An efficient implementation of the PML for truncating FDTD domains

Ramadan¹,

Öztoprak²

2002

Micro & Optical Tech Letters

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NUMERICAL RESULTSFor antenna applications, interest lies mostly in the case of singlebeam radiation. Therefore, the case where only the n ϭ Ϫ1 space harmonic of the TE 01 mode radiates into free space is investigated. In order to verify the effectiveness and suitability of the present approach, we investigate the leakage properties of three grating antennas. Antenna 1, proposed in 1986 [1], is shown in Figure 1(b). Antenna 2 is the proposed omni-directional antenna which is obtained by gloving a uniform shell layer to Antenna I, shown in Figure 1(c). Antenna 3 is the new omni-directional leaky wave antenna with double dielectric gratings, shown in Figure 1(a).Figure 2(a) shows the effect of different antenna structures on the leakage constant. For comparison, the same overall size of these antennas are chosen. The solid lines represent the exact results of the rigorous mode matching method [2,6,7], while the dashed lines are obtained by present perturbation analysis, which agree quite well with the exact results. The increase of the thickness of grating layer (t g1 ) can be viewed as adding more perturbation to the structure. Because of the strong perturbation effect on the guided wave caused by the two grating layers, the leakage constant ␣ of the double grating antenna continues to be larger than that of either single antenna, with or without a shell, for the region of t g1 Ͻ 0.25, and especially in the region of t g1 Ͻ 0.06, where the leakage constant of the double grating antenna is more than ten times those of the single grating antennas. It is seen that the leakage constant of the double grating antenna has been reached when the maximum leakage constant of the single grating, t g1 , is very small. This clearly indicates that under conditions of the same radiation strength, the length of the double grating antenna can be considerably reduced.Figure 2(b) shows variations of the leakage constant with the dielectric constant of the outer grating layer. When the dielectric constant of the outer grating layer is small, the leakage constant increases as the dielectric constant becomes larger. Nevertheless, leakage decreases as the thickness increases further, after 2 ϭ 2.8. This is because the outer grating layer concentrates the fields of the surface wave in the inner grating layer, in this case, the perturbation effect of the inner grating layer on the guided wave is strengthened. However, as the thickness of outer grating layer further increases, the fields of the surface wave enter the shell and outer grating layers and become weaker in the inner grating layer, leakage becomes weaker as well. CONCLUSIONSIn this paper, the leakage characteristics of a new omni-directional leaky-wave antenna with multi-layer structure are analyzed using the improved perturbation method. The analysis of the electromagnetic fields are described in terms of a radial transmission-line network, which brings considerable physical insight into the overall behavior of the leaky-wave antenna. The expression for the leakage constant is g...

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Section: Numerical Studymentioning

confidence: 99%

Section: Numerical Studymentioning

confidence: 99%

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An efficient implementation of the PML for truncating FDTD domains

Ramadan¹,

Öztoprak²

2002

Micro & Optical Tech Letters

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“…The CPU is Intel(R) Pentium (R) 4 CPU 3.00 GHz and the precision of floating point numbers is single. First, the numerical experiment of [8] was attempted in 3-D FDTD domain. We considered the 50 Â 50 Â 51 cells test domain, O T ; with the space and time steps, respectively, 15 mm and 25 ps.…”

Section: Numerical Studymentioning

confidence: 99%

Modified Z‐transform‐based FDTD algorithm for the anisotropic perfectly matched layer

Dai

2007

Int J Numerical Modelling

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SUMMARYA modified Z-transform-based algorithm for implementing the D-H anisotropic perfectly matched layer (APML) is presented for truncating the finite-difference time-domain (FDTD) lattices. The main advantage is that, as compared with the previous Z-transform-based implementation for the D-H APML, the proposed algorithm requires less auxiliary variables in the PML regions, and thus the memory requirement and the computational time are saved. These formulations are simple and independent of the material properties of the FDTD computational domain. Two numerical tests have been carried out to validate these formulations.

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“…For electromagnetics the standard approach uses the Mur boundary conditions, [7]. In [12] high order boundary conditions are tested for the numerical solution of Maxwell's equations.…”

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confidence: 99%