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, the authors summarize the published finite difference formulations for the elastic wave equation and outline their applicability to seafloor problems, where the authors show that finite difference methods are becoming increasingly popular in solving propagation problems as the limitations of other techniques which apply only at high frequency or for flat-lying media become fully appreciated.
Abstract: Understanding seismic wave propagation in realistic seafloor environments is essential for many problems in marine seismology. Finite difference methods are becoming increasingly popular in solving propagation problems as the limitations of other techniques which apply only at high frequency or for flat-lying media become fully appreciated. The seafloor problem, a high contrast in Poisson's ratio at a rough sharp interface, is particularly challenging, and many published formulations fail to solve it accurately. The purpose of this paper is to summarize the published finite difference formulations for the elastic wave equation and to outline their applicability to seafloor problems.
79 citations
TL;DR: In this article, the theory of equivalent operators on Hubert spaces was developed for uniformly elliptic operators and applied to finite element and finite difference discretizations, and the strong and weak forms were considered.
78 citations
TL;DR: In this article, an unconditionally stable mesheless method is proposed with the implementation of the leapfrog alternating-direction-implicit scheme in the 3-D radial point interpolation meshless method.
Abstract: In this paper, an unconditionally stable mesheless method is proposed with the implementation of the leapfrog alternating-direction-implicit scheme in the 3-D radial point interpolation meshless method. The unconditional stability of the proposed method is analytically proven and numerically verified. The accuracy and efficiency of the method are assessed through experiments. Compared with the conventional radial interpolation method, the computational cost can be saved by 85% with little sacrifice of accuracy. The principle presented in this paper can be extended to other existing meshless methods in developing other types of the unconditionally stable meshless methods.
78 citations
TL;DR: In this article, variable mesh difference methods of third order are derived for the solution of the two-point, second-order, singular perturbation problems y = f (x, y, y, e ).
78 citations
TL;DR: In this article, the pseudospectral-Chebyshev method is shown to be convergent in variable coefficient problems and, in some cases, hyperbolic problems.
Abstract: The pseudospectral-Chebyshev methods are shown to be convergent in variable coefficient problems and, in some cases, hyperbolic problems. The analysis demonstrates that the rate of convergence is greater for finite difference methods or the finite element method. For a single first-order hyperbolic equation, the method is seen as remaining stable even when the coefficient changes sign, although in this case it is specified that care must be taken to have adequate spatial resolution. It is noted that this fact, combined with the fact that collocation methods are easy to apply in the nonlinear case, shows that the pseudospectral method is in general preferable to the Galerkin or Tau methods.
78 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |