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 procedure is given that can easily assure the quality of numerical results by obtaining the residual at each point, which can be applied over general or irregular clouds of points.
166 citations
TL;DR: In this paper, the Yee scheme is shown to be second-order convergent on a non-uniform mesh, despite the fact that the local truncation error is only of first order.
Abstract: The Yee scheme is the principal finite difference method used in computing time domain solutions of Maxwell's equations. On a uniform grid the method is easily seen to be second- order convergent in space. This paper shows that the Yee scheme is also second-order convergent on a nonuniform mesh despite the fact that the local truncation error is (nodally) only of first order.
166 citations
TL;DR: In this article, a hybrid scheme based on a set of 2DH extended Boussinesq equations for slowly varying bathymetries is introduced, which combines the finite volume technique, applied to solve the advective part of the equations, with the finite difference method, used to discretize dispersive and source terms.
165 citations
TL;DR: In this paper, a finite-difference method is applied to compute the seismic response of 2D inhomogeneous structures for SH-waves, which allows better adjusted modeling of a medium and yields more efficient computations as compared to those with regular grids.
Abstract: SUMMARY The finite-difference method is applied to compute the seismic response of 2-D inhomogeneous structures for SH-waves. A technique is proposed which uses an irregular grid (a rectangular grid with varying grid spacing). A geological structure may be composed of blocks of media inside of which velocity and density vary linearly in horizontal and vertical directions. The technique allows better adjusted modelling of a medium and, in numerical examples presented, yields more efficient computations as compared to those with regular grids. The technique is tested through comparison with a discrete-wavenumber method. As an example, the seismic response of the sediment-filled Chusal Valley, Carm region, USSR, is computed. The numerical results are compared with observations.
164 citations
TL;DR: In this article, two different approaches for numeri- cal differentiation are considered based on a regularized Volterra equation and disretized version of the regularized VOLTERRA equation.
Abstract: Based on a regularized Volterra equation, two different approaches for numeri- cal differentiation are considered. The first approach consists of solving a regularized Volterra equation while the second approach is based on solving a disretized version of the regularized Volterra equation. Numerical experiments show that these methods are efficient and compete fa- vorably with the variational regularization method for stable calculating the derivatives of noisy functions.
164 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |