A two-dimensional time-domain finite element formulation for periodic structures

Petersson, L.E.R.; Jin, Jian‐Ming

doi:10.1109/tap.2005.844405

Cited by 22 publications

(17 citation statements)

References 9 publications

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“…It is assumed that the weighting function W satisfies a similar periodic boundary condition as the field [39] W Using finite element geometric discretisation the following matrix equation is obtained from (10), (12) and (13) (see (14)) where j = e jv 0 f and j = e −jv 0 f…”

Section: Unit-cell Fefd-mnrbc Formulationmentioning

confidence: 99%

“…Considerable work was done in the frequency-domain finite-element modelling of plane wave scattering from (infinite) planar periodic structures, both two-dimensional (2D) singly periodic and three-dimensional (3D) doubly periodic (for example see [2][3][4][5]) using Floquet's theorem [6]. Subsequently, such 2D and 3D work was extended to the time domain (for example see [7][8][9][10][11][12]). Recently, frequency-domain finite-element research work was done in the area of scattering and radiation from finite planar arrays (for example see [13][14][15][16][17][18][19]).…”

Section: Introductionmentioning

confidence: 99%

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Finite-element time-domain modelling of cylinders with angular periodicity

Bavelis

Mias

2012

IET Microw. Antennas Propag.

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A finite-element time-domain formulation is presented that employs Floquet's theorem to model plane wave scattering from a cylinder with angular periodicity. The proposed methodology is validated through simulations for cylinders with different cross-sections. The results are in good agreement with those obtained from the finite-element frequency-domain method, analytically, from the literature or using commercial software.

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Section: Unit-cell Fefd-mnrbc Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Finite-element time-domain modelling of cylinders with angular periodicity

Bavelis

Mias

2012

IET Microw. Antennas Propag.

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“…Before extensive numerical calculations are performed, the plane wave scattering by a 2-D periodic structure containing cylindrical dielectric rods arrays [32] (relative dielectric constant , diameter is 4 mm, the period is 9 mm, and incident angle is 50 ) was calculated to verify the accuracy of the proposed computer program. We employed the staircase approach to partition the circular cylinders into many very fine rectangular slices.…”

Section: Verification Of the Computer Programmentioning

confidence: 99%

“…The numerical methods for resolving scattering-and guidingcharacteristics, and the electromagnetic fields with the 2-D periodic structures have been well developed. To mention a few, these methods include modal transmission line [23]- [27], generalized scattering matrix [28], lattice-sum for 2-D cylinders array [29], finite-difference time domain [30] and finite-element frequency (and time) domain methods [31], [32].…”

Section: Introductionmentioning

confidence: 99%

Frequency-Selective Transmission by a Leaky Parallel-Plate-Like Waveguide

Hwang

Hsiao

2006

IEEE Trans. Antennas Propagat.

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The phenomena of high frequency-selective transmission of a plane wave by a dielectric two-dimensional (2-D) periodic waveguide, comprising a uniform dielectric layer sandwiched by two finite thickness 2-D periodic structures served as the waveguide wall is described. This structure is termed a leaky parallel-plate-like waveguide because the waveguide walls are not perfect reflection mirrors. The scattering characteristics and dispersion relation, including the phase and attenuation constants, of the 2-D periodic waveguide are thoroughly analyzed with the modal transmission-line method and Floquet theory. The extraordinary open stopbands caused by the contra-flow coupling between a leaky parallel-plate-like waveguide and the leaky waves, which are generated by 2-D periodic structures (waveguide walls), are displayed in the form of the Brillouin diagram. The phase-match condition is used to verify the resonant coupling between the incident plane wave and the leaky parallel-plate-like waveguide modes. Specifically, the transmission peak frequencies are accurately predicted.Index Terms-Frequency selective structure (FSS), leaky parallel-plate-like waveguide, resonant coupling, two-dimensional (2-D) periodic structures.

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“…A number of numerical methods have been developed for the simulation of periodic structures in both frequency and time domains [5,6]. The finite-difference time-domain (FDTD) method is frequently used to analyze periodic structures for it is a transient technique and efficient for wideband applications [7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Implicit-Explicit Spectral FDTD Scheme for Oblique Incidence Problems on Periodic Structures

Mao¹,

Chen²,

Liu³

et al. 2012

PIER

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Abstract-This paper combines a hybrid implicit-explicit (HIE) method with spectral finite-difference time-domain (SFDTD) method for solving periodic structures at oblique incidence, resulting in a HIE-SFDTD method. The new method has the advantages of both HIE-FDTD and SFDTD methods, not only making the stability condition weaker, but also solving the oblique incident wave on periodic structures. Because the stability condition is determined only by two space discretizations in this method, it is extremely useful for periodic problems with very fine structures in one direction. The method replaces the conventional single-angle incident wave with a constant transverse wave-number (CTW) wave, so the fields have no delay in the transverse plane, as a result, the periodic boundary condition (PBC) can be implemented easily for both normal and oblique incident waves. Compared with the ADI-SFDTD method it only needs to solve two untridiagonal matrices when the PBC is applied to, other four equations can be updated directly, while four untridiagonal matrices, two tridiagonal matrices, and six explicit equations should be solved in the ADI-SFDTD method. Numerical examples are presented to demonstrate the efficiency and accuracy of the proposed algorithm. Results show the new algorithm has better accuracy and higher efficiency than that of the ADI-SFDTD method, especially for large time step sizes. The CPU running time for this method can be reduced to about 45% of the ADI-SFDTD method.

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A two-dimensional time-domain finite element formulation for periodic structures

Cited by 22 publications

References 9 publications

Finite-element time-domain modelling of cylinders with angular periodicity

Finite-element time-domain modelling of cylinders with angular periodicity

Frequency-Selective Transmission by a Leaky Parallel-Plate-Like Waveguide

A Hybrid Implicit-Explicit Spectral FDTD Scheme for Oblique Incidence Problems on Periodic Structures

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