A Three-Dimensional Time-Domain Finite-Element Formulation for Periodic Structures

Petersson, L.E.R.; Jin, Jian‐Ming

doi:10.1109/tap.2005.861547

Cited by 56 publications

(21 citation statements)

References 23 publications

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“…Unfortunately, all FETD formulations known to date suffer from the fact that at every time step a matrix inversion has to be carried out which largely off-sets the advantages in CPU-resource usage gained from the finite-element discretization. Nevertheless, recent progress in the FETD of periodic systems [110] and the development of advanced elementary functions for the use with PMLs [111] demonstrate the excellent stability properties of FETD.…”

Section: Finite-element Approachesmentioning

confidence: 99%

Periodic nanostructures for photonics

et al. 2007

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Periodic nanostructures in photonics facilitate a far-reaching control of light propagation and light-matter interaction. This article reviews the current status of this subject, including both recent progress and well-established results. The primary focus is on the basic physical principles and potential applications associated with the existence of Bragg scattering, photonic band structures, and engineered effective-medium properties in periodic dielectric and metallo-dielectric systems. In addition, we discuss advantages and limitations of various theoretical and numerical approaches as well as of those fabrication techniques that have specifically been developed for this field.

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Section: Finite-element Approachesmentioning

confidence: 99%

Periodic nanostructures for photonics

et al. 2007

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“…Recently, much progress has been made in Finite Element Time Domain (FETD) method [8][9][10][11][12], which extends the FEM to time domain. It inherits the advantages of meshing flexibility, material generality and matrices sparseness from FEM and advantages of performing wideband analysis, simulating non-linear and transient phenomena from the time domain method.…”

Section: Introductionmentioning

confidence: 99%

A New 2d Non-Spurious Discontinuous Galerkin Finite Element Time Domain (Dg-Fetd) Method for Maxwell's Equations

Ren¹,

Tobon²,

Liu³

2013

PIER

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Abstract-A new discontinuous Galerkin Finite Element Time Domain (DG-FETD) method for Maxwell's equations is developed. It can suppress spurious modes using basis functions based on polynomials with the same order of interpolation for electric field intensity E and magnetic flux density B. Compared to FETD based on EH scheme, which requires different orders of interpolation polynomials for electric and magnetic field intensities, this method uses fewer unknowns and reduces the computation load. The discontinuous Galerkin method is employed to implement domain decomposition for the EB scheme based FETD. In addition, a well-posed time-domain perfectly matched layer (PML) is extended to the EB scheme to simulate the unbounded problem. Leap frog method is utilized for explicit time stepping. Numerical results demonstrate that the above proposed methods are effective and efficient for 2D time domain TMz multi-domain problems.

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“…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%

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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A Three-Dimensional Time-Domain Finite-Element Formulation for Periodic Structures

Cited by 56 publications

References 23 publications

Periodic nanostructures for photonics

Periodic nanostructures for photonics

A New 2d Non-Spurious Discontinuous Galerkin Finite Element Time Domain (Dg-Fetd) Method for Maxwell's Equations

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

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