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
1 / 2
Papers
TL;DR: In this paper, a method of incorporating lumped terminal conditions into a finite-difference, time-domain (FDTD) analysis of multiconductor transmission lines is given, which provides an exact solution of the transmission-line equations via the FDTD technique when the line discretization, /spl Delta/t, and the time discretisation,/spl Delta /t, are chosen such that /spl delta/t=/spl Delta z/v where v is the phase velocity of propagation on the line.
Abstract: A method of incorporating lumped terminal conditions into a finite-difference, time-domain (FDTD) analysis of multiconductor transmission lines is given. The method provides an exact solution of the transmission-line equations via the FDTD technique when the line discretization, /spl Delta/t, and the time discretization, /spl Delta/t, are chosen such that /spl Delta/t=/spl Delta/z/v where v is the phase velocity of propagation on the line. Examples are given to show that in the case of a multiconductor line in an inhomogeneous medium where the mode velocities are not identical, the method gives accurate results with a minimum of computational effort. >
146 citations
TL;DR: A Fourier pseudo-spectral method that conserves mass and energy is developed for a two-dimensional nonlinear Schrodinger equation and it is proved that the optimal rate of convergence is in the order of O in the discrete L 2 norm without any restrictions on the grid ratio.
146 citations
TL;DR: In this article, the principle of lattice-Boltzmann techniques is recalled and some of the difficulties to simulate convective flows are discussed, and a hybrid scheme with lattice Boltzmann for fluid velocity variables and finite-difference for the temperature is proposed.
146 citations
TL;DR: In this article, a compact central-difference approximation in conjunction with the Yee (1966) grid is used to compute the spatial derivatives in Maxwell's equations, and the four-stage Runge-Kutta (RK) integrator is invoked.
Abstract: A compact central-difference approximation in conjunction with the Yee (1966) grid is used to compute the spatial derivatives in Maxwell's equations. To advance the semi-discrete equations, the four-stage Runge-Kutta (RK) integrator is invoked. This combination of spatial and temporal differencing leads to a scheme that is fourth-order accurate, conditionally stable, and highly efficient. Moreover, the use of compact differencing allows one to apply the compact operator in the vicinity of a perfect conductor-an attribute not found in other higher order methods. Results are provided that quantify the spectral properties of the method. Simulations are conducted on problem spaces that span one and three dimensions and whose domains are of the open and closed type. Results from these simulations are compared with exact closed-form solutions; the agreement between these results is consistent with numerical analysis.
145 citations
Book•
9 Nov 1995
TL;DR: In this article, the authors present a FORTRANet program for simulating groundwater flow and quality in a Porous Media environment, using finite difference methods and finite element methods for solving hydrodynamic dispersion equations.
Abstract: Contents: Introduction.- Hydrodynamic Dispersion in Porous Media.- Analytical Solutions of Hydrodynamic Dispersion Equations.- Finite Difference Methods and the Method of Characteristics for Hydrodynamic Dispersion Equations.- Finite Element Methods for Solving Hydrodynamic Dispersion Equations.- Numerical Solutions of Advection-Dominated Problems.- Mathematical Models of Groundwater Quality.- Applications of Groundwater Quality Models.- Conclusions.- Appendix A: The Related Parameters in the Modeling of Mass Transport in Porous Media.- Appendix B: A FORTRAN Program for Simultaneously Simulating Groundwater Flow and Quality.- References.
145 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |