Topic

# Finite-difference time-domain method

About: Finite-difference time-domain method is a research topic. Over the lifetime, 12306 publications have been published within this topic receiving 166903 citations. The topic is also known as: Yee's method & FDTD.

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31 May 1995

TL;DR: This paper presents background history of space-grid time-domain techniques for Maxwell's equations scaling to very large problem sizes defense applications dual-use electromagnetics technology, and the proposed three-dimensional Yee algorithm for solving these equations.

Abstract: Part 1 Reinventing electromagnetics: background history of space-grid time-domain techniques for Maxwell's equations scaling to very large problem sizes defense applications dual-use electromagnetics technology. Part 2 The one-dimensional scalar wave equation: propagating wave solutions finite-difference approximation of the scalar wave equation dispersion relations for the one-dimensional wave equation numerical group velocity numerical stability. Part 3 Introduction to Maxwell's equations and the Yee algorithm: Maxwell's equations in three dimensions reduction to two dimensions equivalence to the wave equation in one dimension. Part 4 Numerical stability: TM mode time eigenvalue problem space eigenvalue problem extension to the full three-dimensional Yee algorithm. Part 5 Numerical dispersion: comparison with the ideal dispersion case reduction to the ideal dispersion case for special grid conditions dispersion-optimized basic Yee algorithm dispersion-optimized Yee algorithm with fourth-order accurate spatial differences. Part 6 Incident wave source conditions for free space and waveguides: requirements for the plane wave source condition the hard source total-field/scattered field formulation pure scattered field formulation choice of incident plane wave formulation. Part 7 Absorbing boundary conditions for free space and waveguides: Bayliss-Turkel scattered-wave annihilating operators Engquist-Majda one-way wave equations Higdon operator Liao extrapolation Mei-Fang superabsorption Berenger perfectly-matched layer (PML) absorbing boundary conditions for waveguides. Part 8 Near-to-far field transformation: obtaining phasor quantities via discrete fourier transformation surface equivalence theorem extension to three dimensions phasor domain. Part 9 Dispersive, nonlinear, and gain materials: linear isotropic case recursive convolution method linear gyrontropic case linear isotropic case auxiliary differential equation method, Lorentz gain media. Part 10 Local subcell models of the fine geometrical features: basis of contour-path FD-TD modelling the simplest contour-path subcell models the thin wire conformal modelling of curved surfaces the thin material sheet relativistic motion of PEC boundaries. Part 11 Explicit time-domain solution of Maxwell's equations using non-orthogonal and unstructured grids, Stephen Gedney and Faiza Lansing: nonuniform, orthogonal grids globally orthogonal global curvilinear co-ordinates irregular non-orthogonal unstructured grids analysis of printed circuit devices using the planar generalized Yee algorithm. Part 12 The body of revolution FD-TD algorithm, Thomas Jurgens and Gregory Saewert: field expansion difference equations for on-axis cells numerical stability PML absorbing boundary condition. Part 13 Modelling of electromagnetic fields in high-speed electronic circuits, Piket-May and Taflove. (part contents).

11,194 citations

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TL;DR: This paper describes Meep, a popular free implementation of the finite-difference time-domain (FDTD) method for simulating electromagnetism, and focuses on aspects of implementing a full-featured FDTD package that go beyond standard textbook descriptions of the algorithm.

2,489 citations

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04 May 2018

TL;DR: In this paper, the authors define the fundamental concepts of scattered field FDTD and its application in a wide range of applications including: Coupling Effects Coupling effects Waveguide Aperture Coupling Lossy Dielectric Scattering Special Capabilities Far Zone Transformation Frequency Dependent Materials Surface Impedance Subcellular Extensions Nonlinear Loads and Materials Visualization Advanced Applications Far Zone Scattering Antennas Gyrotropic Media Mathematical Basis of FDTD, and Alternate Methods Difference Equations in General Stability, Dispersion, Accuracy Outer Radiation Boundary Conditions Alternate Formulations

Abstract: Fundamental Concepts Scattered Field FDTD Formulation FDTD Basics Basic Applications Coupling Effects Waveguide Aperture Coupling Lossy Dielectric Scattering Special Capabilities Far Zone Transformation Frequency Dependent Materials Surface Impedance Subcellular Extensions Nonlinear Loads and Materials Visualization Advanced Applications Far Zone Scattering Antennas Gyrotropic Media Mathematical Basis of FDTD and Alternate Methods Difference Equations in General Stability, Dispersion, Accuracy Outer Radiation Boundary Conditions Alternate Formulations Appendix A: Other Coordinate Systems and Reduced Dimensions Appendix B: FORTRAN Listings

2,266 citations

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TL;DR: A modified set of Maxwell's equations is presented that includes complex coordinate stretching along the three Cartesian coordinates that allow the specification of absorbing boundaries with zero reflection at all angles of incidence and all frequencies.

Abstract: A modified set of Maxwell's equations is presented that includes complex coordinate stretching along the three Cartesian coordinates. The added degrees of freedom in the modified Maxwell's equations allow the specification of absorbing boundaries with zero reflection at all angles of incidence and all frequencies. The modified equations are also related to the perfectly matched layer that was presented recently for 2D wave propagation. Absorbing-material boundary conditions are of particular interest for finite-difference time-domain (FDTD) computations on a single-instruction multiple-data (SIMD) massively parallel supercomputer. A 3D FDTD algorithm has been developed on a connection machine CM-5 based on the modified Maxwell's equations and simulation results are presented to validate the approach. © 1994 John Wiley & Sons, Inc.

1,660 citations

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TL;DR: In this paper, a mushroom-like E-plane coupled E-strip antenna array on a thick and high permittivity substrate has been analyzed using the finite-difference time-domain (FDTD) method.

Abstract: Utilization of electromagnetic band-gap (EBG) structures is becoming attractive in the electromagnetic and antenna community. In this paper, a mushroom-like EBG structure is analyzed using the finite-difference time-domain (FDTD) method. Its band-gap feature of surface-wave suppression is demonstrated by exhibiting the near field distributions of the electromagnetic waves. The mutual coupling of microstrip antennas is parametrically investigated, including both the E and H coupling directions, different substrate thickness, and various dielectric constants. It is observed that the E-plane coupled microstrip antenna array on a thick and high permittivity substrate has a strong mutual coupling due to the pronounced surface waves. Therefore, an EBG structure is inserted between array elements to reduce the mutual coupling. This idea has been verified by both the FDTD simulations and experimental results. As a result, a significant 8 dB mutual coupling reduction is noticed from the measurements.

1,394 citations