Finite-difference time-domain modeling of curved surfaces (EM scattering)

Jurgens, T.G.; Taflove, Allen; Umashankar, K.R.; Moore, Tirin

doi:10.1109/8.138836

Cited by 318 publications

(127 citation statements)

References 15 publications

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“…The conformal FDTD method on non-orthogonal grids [15][16][17], counter path FDTD method [18,19], and subgridding method [20][21][22] can represent curved interfaces suitably, but they are relatively difficult to implement and increase the memory and computation time. A different approach using effective permittivities (EPs), which derives from interface interpolations based on Ampere's and Faraday's integration laws, can reduce the error of the permittivity model on coarse grids in a simple implementation and at low computational cost [23][24][25][26][27][28][29][30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Effective Permittivity for FDTD Calculation of Plasmonic Materials

Okada

Cole

2012

Micromachines

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We present a new effective permittivity (EP) model to accurately calculate surface plasmons (SPs) using the finite-difference time-domain (FDTD) method. The computational representation of physical structures with curved interfaces causes inherent errors in FDTD calculations, especially when the numerical grid is coarse. Conventional EP models improve the errors, but they are not effective for SPs because the SP resonance condition determined by the original permittivity is changed by the interpolated EP values. We perform FDTD simulations using the proposed model for an infinitely-long silver cylinder and gold sphere, and the results are compared with Mie theory. Our model gives better accuracy than the conventional staircase and EP models for SPs.

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Section: Introductionmentioning

confidence: 99%

Effective Permittivity for FDTD Calculation of Plasmonic Materials

Okada

Cole

2012

Micromachines

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“…For broadband applications and problems including material interface, wave scattering and penetration over large and complex domains, the grid size required by using the FDTD method could become prohibitively expensive for modern computers. Much progress has been made in the past two decades in improving the FDTD method, including plentiful methods for removing the staircased approximation for boundaries and geometries, [5][6][7][8][9] and numerous high-order FDTD methods [3,[10][11][12][13][14][15][16]. Here, by high order we refer to orders being higher than three, which are essential for modern problems of moderately high frequency (short) waves and/or large domain in nature.…”

Section: Introductionmentioning

confidence: 99%

High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces

Zhao

Wang

2004

Journal of Computational Physics

197

164

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This paper introduces a series of novel hierarchical implicit derivative matching methods to restore the accuracy of high-order finite difference time-domain (FDTD) schemes of computational electromagnetics (CEM) with material interfaces in one (1D) and two spatial dimensions (2D). By making use of fictitious points, systematic approaches are proposed to locally enforce the physical jump conditions at material interfaces in a preprocessing stage, to arbitrarily high orders of accuracy in principle. While often limited by numerical instability, orders up to 16 in 1D and 2D are achieved. Detailed stability analyses are presented for the present approach to examine the up limit in constructing embedded FDTD methods. As natural generalizations of the high-order FDTD schemes, the proposed derivative matching methods automatically reduce to the standard FDTD schemes when the material interfaces are absent. An interesting feature of the present approach is that it encompasses a variety of schemes of different orders in a single code. Another feature of the present approach is that it can be robustly implemented with other high accuracy time-domain approaches, such as the multiresolution time-domain (MRTD) method and the local spectral time-domain (LSTD) method, to cope 1 with material interfaces. Numerical experiments on both 1D and 2D problems are carried out to test the convergence, examine the stability, access the efficiency, and explore the limitation of the proposed methods. It is found that operating at their best capacity, the proposed high order schemes are at least a million times more efficient than their fourth order versions in both 1D and 2D. Therefore, it is believed that the proposed hierarchical derivative matching methods are highly accurate, efficient, and robust for CEM.

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“…Generalization of this approach assuming local curvilinear coordinates for cell faces was achieved by Lee et al [8]. In this respect, a number of alternate FDTD methods have also been proposed, such as the contour path FDTD [9], discrete surface integral FDTD [10], and nonorthogonal FDTD [11], in generalized curvilinear coordinates by using conformal meshes instead of staircasing for curved surfaces.…”

Section: Introductionmentioning

confidence: 99%

Wavefront-ray grid FDTD algorithm

Çiydem¹,

Koc²

2016

Turk J Elec Eng & Comp Sci

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Abstract:A finite difference time domain algorithm on a wavefront-ray grid (WRG-FDTD) is proposed in this study to reduce numerical dispersion of conventional FDTD methods. A FDTD algorithm conforming to a wavefront-ray grid can be useful to take into account anisotropy effects of numerical grids since it features directional energy flow along the rays. An explicit and second-order accurate WRG-FDTD algorithm is provided in generalized curvilinear coordinates for an inhomogeneous isotropic medium. Numerical simulations for a vertical electrical dipole have been conducted to demonstrate the benefits of the proposed method. Results have been compared with those of the spherical FDTD algorithm and it is showed that numerical grid anisotropy can be reduced highly by WRG-FDTD.

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Finite-difference time-domain modeling of curved surfaces (EM scattering)

Cited by 318 publications

References 15 publications

Effective Permittivity for FDTD Calculation of Plasmonic Materials

Effective Permittivity for FDTD Calculation of Plasmonic Materials

High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces

Wavefront-ray grid FDTD algorithm

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