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
Book•
12 Dec 2001
TL;DR: In this article, a survey of higher-order finite difference methods for wave equations is presented, and various mass-lumped finite element methods for the transient wave equations, and the most efficient methods for each sort of problem are presented.
Abstract: Solving efficiently the wave equations involved in modeling acoustic, elastic or electromagnetic wave propagation remains a challenge both for research and industry. To attack the problems coming from the propagative character of the solution, the author constructs higher-order numerical methods to reduce the size of the meshes, and consequently the time and space stepping, dramatically improving storage and computing times. This book surveys higher-order finite difference methods and develops various mass-lumped finite (also called spectral) element methods for the transient wave equations, and presents the most efficient methods, respecting both accuracy and stability for each sort of problem. A central role is played by the notion of the dispersion relation for analyzing the methods. The last chapter is devoted to unbounded domains which are modeled using perfectly matched layer (PML) techniques. Numerical examples are given.
738 citations
TL;DR: In this article, a finite-difference scheme for direct simulation of the incompressible time-dependent three-dimensional Navier-Stokes equations in cylindrical coordinates is presented.
722 citations
TL;DR: The integrated finite difference method (IFDM) as mentioned in this paper is a powerful numerical technique for solving problems of groundwater flow in porous media, which combines the advantages of an integral formulation with the simplicity of finite difference gradients and is convenient for handling multidimensional heterogeneous systems composed of isotropic materials.
Abstract: The theoretical basis for the integrated finite difference method (IFDM) is presented to describe a powerful numerical technique for solving problems of groundwater flow in porous media. The method combines the advantages of an integral formulation with the simplicity of finite difference gradients and is very convenient for handling multidimensional heterogeneous systems composed of isotropic materials. Three illustrative problems are solved to demonstrate that two- and three-dimensional problems are handled with equal ease. Comparison of IFDM with the well-known finite element method (FEM) indicates that both are conceptually similar and differ mainly in the procedure adopted for measuring spatial gradients. The IFDM includes a simple criterion for local stability and an efficient explicit-implicit iterative scheme for marching in the time domain. If such a scheme can be incorporated in a new version of FEM, it should be possible to develop an improved numerical technique that combines the inherent advantages of both methods.
715 citations
TL;DR: In this article, an unconditionally stable three-dimensional (3-D) finite-difference time-method (FDTD) is presented where the time step used is no longer restricted by stability but by accuracy.
Abstract: In this paper, an unconditionally stable three-dimensional (3-D) finite-difference time-method (FDTD) is presented where the time step used is no longer restricted by stability but by accuracy. The principle of the alternating direction implicit (ADI) technique that has been used in formulating an unconditionally stable two-dimensional FDTD is applied. Unlike the conventional ADI algorithms, however, the alternation is performed in respect to mixed coordinates rather than to each respective coordinate direction, Consequently, only two alternations in solution marching are required in the 3-D formulations. Theoretical proof of the unconditional stability is shown and numerical results are presented to demonstrate the effectiveness and efficiency of the method. It is found that the number of iterations with the proposed FDTD can be at least four times less than that with the conventional FDTD at the same level of accuracy.
703 citations
TL;DR: This paper analyzes the runtime of algorithms by counting the number of operations in a loop and finds the total number of instructions is given by where T 1 is the time for loop increment and comparison.
Abstract: Motivation When we analyze the runtime of algorithms, we simply count the number of operations. For example, the following loop for k = 1 to n do square(k); where square(k) is a function that has running time T 2 k 2. Then the total number of instructions is given by where T 1 is the time for loop increment and comparison.
651 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |