A selective survey of the finite-difference time-domain literature

Shlager, K.L.; Schneider, John B.

doi:10.1109/74.414731

Cited by 188 publications

(84 citation statements)

References 290 publications

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“…The first results concerning this approach were presented in [70]. References to the later investigations can be found in review [59].…”

Section: Problem Formulationmentioning

confidence: 99%

Finite-difference Approximation of Mathematical Physics Problems on Irregular Grids

Vabishchevich¹

2005

Comput. Methods Appl. Math.

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-Mathematical physics problems are often formulated by means of the vector analysis differential operators: divergence, gradient and rotor. For approximate solutions of such problems it is natural to use the corresponding operator statements for the grid problems, i.e., to use the so-called VAGO (Vector Analys Grid Operators) method. In this paper, we discuss the possibilities of such an approach in using general irregular grids. The vector analysis difference operators are constructed using the Delaunay triangulation and the Voronoi diagrams. The truncation error and the consistency property of the difference operators constructed on two types of grids are investigated. Construction and analysis of the difference schemes of the VAGO method for applied problems are illustrated by the examples of stationary and non-stationary convection-diffusion problems. The other examples concerned the solution of the nonstationary vector problems described by the second-order equations or the systems of first-order equations.2000 Mathematics Subject Classification: 65N06; 65M06.

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“…The first results concerning this approach were presented in [70]. References to the later investigations can be found in review [59].…”

Section: Problem Formulationmentioning

confidence: 99%

Finite-difference Approximation of Mathematical Physics Problems on Irregular Grids

Vabishchevich¹

2005

Comput. Methods Appl. Math.

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“…4 Generally, numerical methods such as the T-matrix method, 18 the discrete dipole approximation 19 ͓Fig. 2͑b͔͒, or finite-difference time-domain simulations 20 have to be used to calculate the resonance frequencies and mode profiles of more complex shapes. Such simulations have especially been employed to determine the local-field enhancement at the particle surface, in conjunction with discussions of enhancements of nonlinear processes and surface-enhanced Raman scattering ͑SERS͒ as discussed below.…”

Section: ͑2͒mentioning

confidence: 99%

Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures

Maier

Atwater

2005

Journal of Applied Physics

1,800

1,217

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We review the basic physics of surface-plasmon excitations occurring at metal/dielectric interfaces with special emphasis on the possibility of using such excitations for the localization of electromagnetic energy in one, two, and three dimensions, in a context of applications in sensing and waveguiding for functional photonic devices. Localized plasmon resonances occurring in metallic nanoparticles are discussed both for single particles and particle ensembles, focusing on the generation of confined light fields enabling enhancement of Raman-scattering and nonlinear processes. We then survey the basic properties of interface plasmons propagating along flat boundaries of thin metallic films, with applications for waveguiding along patterned films, stripes, and nanowires. Interactions between plasmonic structures and optically active media are also discussed.

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“…One technique, the finite difference time domain (FDTD) method, as first proposed by Yee [1966] and further advocated by Taftore and Brodwin [1975], has emerged as a leading methodology, as manifested by voluminous publications that have come into print [Shlager and Schneider, 1995]. For example, the method has been applied to problems associated with radar crosssectional analysis [ Taftore and Umashankar, 1983], electromagnetic human exposure studies [Gandhi and Furse, 1997], and ionospheric propagation studies [Young, 1994], to name a few.…”

Section: Introductionmentioning

confidence: 99%

High‐order, leapfrog methodology for the temporally dependent Maxwell's equations

Young¹

2001

Radio Science

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Abstract.A high-order, leapfrog integrator is presented and analyzed for Maxwell's time domain equations. The integrator is shown to be quite robust in terms of its efficiency and memory demands. Moreover, the integrator retains the original simplicity of the traditional second-order, leapfrog integrator. Rigorous Fourier analyses are presented to quantify the dispersion, dissipation, and stability properties of the integrator. To limit the scope of the presentation, the 2x2, 2x4, 4x2, and 4x4 schemes are examined and compared. Here the first digit denotes temporal accuracy; the second digit denotes spatial accuracy. Numerical demonstrations, using the three-dimensional rectangular waveguide as the object under test, are provided to further substantiate the theoretical analysis.

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A selective survey of the finite-difference time-domain literature

Cited by 188 publications

References 290 publications

Finite-difference Approximation of Mathematical Physics Problems on Irregular Grids

Finite-difference Approximation of Mathematical Physics Problems on Irregular Grids

Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures

High‐order, leapfrog methodology for the temporally dependent Maxwell's equations

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