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 paper, a 2D velocity-stress, finite-difference scheme simulates waves within poroelastic media as described by Biot's theory is presented, and a series of numerical experiments that are compared to exact analytical solutions allow the authors to assess the stability conditions and dispersion relations of the explicit POROELAS method.
Abstract: Numerical modeling of seismic waves in heterogeneous, porous reservoir rocks is an important tool for interpreting seismic surveys in reservoir engineering. Various theoretical studies derive effective elastic moduli and seismic attributes from complex rock properties, involving patchy saturation and fractured media. To confirm and further develop rock-physics theories for reservoir rocks, accurate numerical modeling tools are required. Our 2D velocity-stress, finite-difference scheme simulates waves within poroelastic media as described by Biot’s theory. The scheme is second order in time, contains high-order spatial derivative operators, and is parallelized using the domain-decomposition technique. A series of numerical experiments that are compared to exact analytical solutions allow us to assess the stability conditions and dispersion relations of the explicit poroelastic finite-differ-ence method. The focus of the experiments is to model wave-induced flow accurately in the vicinity of mesoscopic hete...
101 citations
TL;DR: In this article, a hybrid central finite difference-WENO scheme was proposed for the solution of conservation laws, in particular, those related to shock-turbulence interaction problems.
101 citations
TL;DR: In this article, an one-step arbitrary-order leapfrog alternating-direction-implicit finite-difference time domain (ADI-FDTD) method is presented and its unconditional stability is analytically proven and numerically verified.
Abstract: An one-step arbitrary-order leapfrog alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method is presented. Its unconditional stability is analytically proven and numerically verified. Its numerical properties are shown to be identical to those of the conventional ADI-FDTD and LOD-FDTD methods. However, its computational expenditure is found to be the lowest. In other words, in comparison with the ADI-FDTD and LOD-FDTD methods, the one-step arbitrary-order leap-frog ADI-FDTD method retains identical numerical modeling accuracy but with higher computational efficiency.
101 citations
Journal Article•
TL;DR: In this article, the stability and convergence of fractional finite difference methods with respect to the generalized discrete Gronwall inequality (GDFI) was analyzed. But the authors did not consider the high order methods based on convolution.
Abstract: Fractional finite difference methods are useful to solve the fractional differential equations. The aim of this article is to prove the stability and convergence of the fractional Euler method, the fractional Adams method and the high order methods based on the convolution formula by using the generalized discrete Gronwall inequality. Numerical experiments are also presented, which verify the theoretical analysis.
101 citations
101 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |