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 massively parallel method for computing first arrival times in arbitrary velocity models is presented, which relies on a systematic application of Huygens' principle in the finite difference approximation.
Abstract: SUMMARY We present a new massively parallel method for computation of first arrival times in arbitrary velocity models. An implementation on conventional sequential computers is also proposed. This method relies on a systematic application of Huygens’ principle in the finite difference approximation. Such an approach explicitly takes into account the existence of different propagation modes (transmitted and diffracted body waves, head waves). Local discontinuities of the time gradient in the first arrival time field (e.g., caustics) are built as intersections of locally independent wavefronts. As a consequence, the proposed method provides accurate first traveltimes in the presence of extremely severe, arbitrarily shaped velocity contrasts. Associated with a simple procedure which accurately traces rays in the obtained time field, this method provides a very fast tool for a large spectrum of seismic and seismological problems. We show moreover that this method may also be used to obtain several arrivals at a given receiver, when the model contains reflectors. This possibility significantly extends the domain of potential geophysical applications.
962 citations
TL;DR: In this paper, a multiple interacting continua method (MINC) is proposed for numerical simulation of heat and multi-phase fluid flow in multidimensional, fractured porous media.
Abstract: A Multiple Interacting Continua method (MINC) is presented which is applicable for numerical simulation of heat and multi-phase fluid flow in multidimensional, fractured porous media. This method is a generalization of the double-porosity concept. The partitioning of the flow domain into computational volume elements is based on the criterion of approximate thermodynamic equilibrium at all times within each element. The thermodynamic conditions in the rock matrix are assumed to be primarily controlled by the distance from the fractures, which leads to the use of nested grid blocks. The MINC concept is implemented through the Integral Finite Difference (IFD) method. No analytical approximations are made for the coupling between the fracture and matrix continua. Instead, the transient flow of fluid and heat between matrix and fractures is treated by a numerical method. The geometric parameters needed in a simulation are preprocessed from a specification of fracture spacings and apertures, and the geometry of the matrix blocks. The MINC method is verified by comparison with the analytical solution of Warren and Root. Illustrative applications are given for several geothermal reservoir engineering problems.
953 citations
TL;DR: Eulerian finite difference methods based on a level set formulation derived for incompressible, immiscible Navier?Stokes equations are proposed and are capable of computing interface singularities such as merging and reconnection.
930 citations
TL;DR: In this article, an accurate description for the dispersion of gold in the range of 1.24 -2.48 eV was proposed and implemented in an FDTD algorithm and evaluated its efficiency by comparison with an analytical method.
Abstract: We propose an accurate description for the dispersion of gold in the range of 1.24--2.48 eV. We implement this improved model in an FDTD algorithm and evaluate its efficiency by comparison with an analytical method. Extinction spectra of gold nanoparticle arrays are then calculated.
865 citations
TL;DR: The final convergence result shows clearly how the regularity of the solution and the grading of the mesh affect the order of convergence of the difference scheme, so one can choose an optimal mesh grading.
Abstract: A reaction-diffusion problem with a Caputo time derivative of order $\alpha\in (0,1)$ is considered. The solution of such a problem is shown in general to have a weak singularity near the initial time $t=0$, and sharp pointwise bounds on certain derivatives of this solution are derived. A new analysis of a standard finite difference method for the problem is given, taking into account this initial singularity. This analysis encompasses both uniform meshes and meshes that are graded in time, and includes new stability and consistency bounds. The final convergence result shows clearly how the regularity of the solution and the grading of the mesh affect the order of convergence of the difference scheme, so one can choose an optimal mesh grading. Numerical results are presented that confirm the sharpness of the error analysis.
857 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |