Topic
Finite difference method
About: Finite difference method is a research topic. Over the lifetime, 21603 publications have been published within this topic receiving 468852 citations. The topic is also known as: Finite-difference methods & FDM.
Papers published on a yearly basis
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Papers
TL;DR: In this article, a general formulation for finite-difference time-domain (FDTD) modeling of wave propagation in arbitrary frequency-dispersive media is presented, and two algorithmic approaches are outlined for incorporating dispersion into the FDTD time-stepping equations.
Abstract: A general formulation is presented for finite-difference time-domain (FDTD) modeling of wave propagation in arbitrary frequency-dispersive media. Two algorithmic approaches are outlined for incorporating dispersion into the FDTD time-stepping equations. The first employs a frequency-dependent complex permittivity (denoted Form-1), and the second employs a frequency-dependent complex conductivity (denoted Form-2). A Pade representation is used in Z-transform space to represent the frequency-dependent permittivity (Form-1) or conductivity (Form-2). This is a generalization over several previous methods employing either Debye, Lorentz, or Drude models. The coefficients of the Pade model may be obtained through an optimization process, leading directly to a finite-difference representation of the dispersion relation, without introducing discretization error. Stability criteria for the dispersive FDTD algorithms are given. We show that several previously developed dispersive FDTD algorithms can be cast as special cases of our more general framework. Simulation results are presented for a one-dimensional (1-D) air/muscle example considered previously in the literature and a three-dimensional (3-D) radiation problem in dispersive, lossy soil using measured soil data.
193 citations
TL;DR: In this article, the field evolution along longitudinally nonuniform finite-cladding fibers of circularly symmetric cross section was analyzed in terms of coupled modes, where local modes were used for abruptly tapered fibers, whereas linear-index fiber modes provided the expansion basis for Kerr-type nonlinear-index fibers.
Abstract: Field evolution along longitudinally nonuniform finite-cladding fibers of circularly symmetric cross section is analyzed in terms of coupled modes. Local modes are used for abruptly tapered fibers, whereas linear-index fiber modes provide the expansion basis for Kerr-type nonlinear-index fibers. Convergence of the results suggests in both cases that only a finite number of bound modes is sufficient to describe the field adequately. A comparison with simulations given by a finite-difference beam-propagation method that was developed for circularly symmetric waveguides confirms the validity of this assumption.
193 citations
TL;DR: In this article, an efficient finite-difference time-domain algorithm (FDTD) is presented for solving Maxwell's equations with rotationally symmetric geometries, which enables us to employ a two-dimensional difference lattice by projecting the three-dimensional (3-D) Yee-cell in cylindrical coordinates (r, /spl phi/, z) onto the r-z plane.
Abstract: In this paper, an efficient finite-difference time-domain algorithm (FDTD) is presented for solving Maxwell's equations with rotationally symmetric geometries. The azimuthal symmetry enables us to employ a two-dimensional (2-D) difference lattice by projecting the three-dimensional (3-D) Yee-cell in cylindrical coordinates (r, /spl phi/, z) onto the r-z plane. Extensive numerical results have been derived for various cavity structures and these results have been compared with those available in the literature. Excellent agreement has been observed for all of the cases investigated.
192 citations
TL;DR: High-order finite difference methods for solving the Helmholtz equation are developed and analyzed, in one and two dimensions on uniform grids, and a symmetric high-order representation is developed for a Neumann boundary condition.
191 citations
TL;DR: Li and Yu as discussed by the authors developed a three-dimensional numerical model based on the full Navier-Stokes equations (NSE) in σ-coordinate to simulate two-dimensional solitary waves propagating in constant depth.
Abstract: A three-dimensional numerical model based on the full Navier–Stokes equations (NSE) in σ-coordinate is developed in this study. The σ-coordinate transformation is first introduced to map the irregular physical domain with the wavy free surface and uneven bottom to the regular computational domain with the shape of a rectangular prism. Using the chain rule of partial differentiation, a new set of governing equations is derived in the σ-coordinate from the original NSE defined in the Cartesian coordinate. The operator splitting method (Li and Yu, Int. J. Num. Meth. Fluids 1996; 23: 485–501), which splits the solution procedure into the advection, diffusion, and propagation steps, is used to solve the modified NSE. The model is first tested for mass and energy conservation as well as mesh convergence by using an example of water sloshing in a confined tank. Excellent agreements between numerical results and analytical solutions are obtained. The model is then used to simulate two- and three-dimensional solitary waves propagating in constant depth. Very good agreements between numerical results and analytical solutions are obtained for both free surface displacements and velocities. Finally, a more realistic case of periodic wave train passing through a submerged breakwater is simulated. Comparisons between numerical results and experimental data are promising. The model is proven to be an accurate tool for consequent studies of wave-structure interaction. Copyright © 2002 John Wiley & Sons, Ltd.
191 citations
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Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |