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: The results obtained demonstrate that the FDTD method is capable of calculating internal SAR distribution with acceptable accuracy and is evaluated by comparing its results to analytic solutions in two and three dimensions.
Abstract: Although there are acceptable methods for calculating whole body electromagnetic absorption, no completely acceptable method for calculating the local specific absorption rate (SAR) at points within the body has been developed. Frequency domain methods, such as the method of moments (MoM) have achieved some success; however, MoM requires computer storage on the order of (3N) 2 and computation time on the order of (3N) 3 where N is the number of cells. The finite-difference time-domain (FDTD) method has been employed extensively in calculating the scattering of metallic objects, and recently is seeing some use in calculating the interaction of EM fields with complex, lossy dielectric bodies. Since the FDTD method has storage and time requirements proportional to N, it presents an attractive alternative to calculating SAR distribution in large bodies. This paper describes the FDTD method and evaluates it by comparing its results to analytic solutions in two and three dimensions. The utility of the FDTD method is demonstrated by a 3D scan of the human torso. The results obtained demonstrate that the FDTD method is capable of calculating internal SAR distribution with acceptable accuracy. With the availability of supercomputers, such as the CRAY II, the calculation of SAR distribution in a man model of 50 000 cells (1.27 cm per cell) appears to be feasible.
187 citations
TL;DR: In this article, the Tiwari and Das model with new more realistic empirical correlations for the physical properties of the nanofluids has been used for numerical analysis and the governing equations have been solved numerically on the basis of a second-order accurate finite difference method.
Abstract: Free convection in a square differentially heated porous cavity filled with a nanofluid is numerically investigated. The mathematical model has been formulated in dimensionless stream function and temperature taking into account the Darcy–Boussinesq approximation. The Tiwari and Das’ nanofluid model with new more realistic empirical correlations for the physical properties of the nanofluids has been used for numerical analysis. The governing equations have been solved numerically on the basis of a second-order accurate finite difference method. The developed algorithm has been validated by direct comparisons with previously published papers and the results have been found to be in good agreement. The results have been presented in terms of the streamlines, isotherms, local, and average Nusselt numbers at left vertical wall at a wide range of key parameters.
186 citations
TL;DR: A systematic approach is presented that enables ''energy stable'' modifications for existing WENO schemes of any order and develops new weight functions and derive constraints on their parameters, which provide consistency, much faster convergence of the high-order ESWenO schemes to their underlying linear schemes for smooth solutions with arbitrary number of vanishing derivatives, and better resolution near strong discontinuities than the conventional counterparts.
186 citations
Posted Content•
TL;DR: By successfully applying diffusion to LSE, the RD-LSE model is stable by means of the simple finite difference method, which is very easy to implement.
Abstract: This paper presents a novel reaction-diffusion (RD) method for implicit active contours, which is completely free of the costly re-initialization procedure in level set evolution (LSE). A diffusion term is introduced into LSE, resulting in a RD-LSE equation, to which a piecewise constant solution can be derived. In order to have a stable numerical solution of the RD based LSE, we propose a two-step splitting method (TSSM) to iteratively solve the RD-LSE equation: first iterating the LSE equation, and then solving the diffusion equation. The second step regularizes the level set function obtained in the first step to ensure stability, and thus the complex and costly re-initialization procedure is completely eliminated from LSE. By successfully applying diffusion to LSE, the RD-LSE model is stable by means of the simple finite difference method, which is very easy to implement. The proposed RD method can be generalized to solve the LSE for both variational level set method and PDE-based level set method. The RD-LSE method shows very good performance on boundary anti-leakage, and it can be readily extended to high dimensional level set method. The extensive and promising experimental results on synthetic and real images validate the effectiveness of the proposed RD-LSE approach.
186 citations
TL;DR: In this article, a numerical finite difference scheme was proposed to simulate the motion of a damped, stiff string interacting with a nonlinear hammer, from which the time histories of string displacement and velocity for each point of the string were computed in the time domain.
Abstract: The first attempt to generate musical sounds by solving the equations of vibrating strings by means of finite difference methods (FDM) was made by Hiller and Ruiz [J. Audio Eng. Soc. 19, 462–472 (1971)]. It is shown here how this numerical approach and the underlying physical model can be improved in order to simulate the motion of the piano string with a high degree of realism. Starting from the fundamental equations of a damped, stiff string interacting with a nonlinear hammer, a numerical finite difference scheme is derived, from which the time histories of string displacement and velocity for each point of the string are computed in the time domain. The interacting force between hammer and string, as well as the force acting on the bridge, are given by the same scheme. The performance of the model is illustrated by a few examples of simulated string waveforms. A brief discussion of the aspects of numerical stability and dispersion with reference to the proper choice of sampling parameters is also included.
185 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |