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 ADE-CPML method provides a more flexible representation that can be extended to higher-order methods and is applied to the discontinuous Galerkin finite element time-domain method.
Abstract: An efficient auxiliary-differential equation (ADE) form of the complex frequency shifted perfectly matched layer (CPML) absorbing media derived from a stretched coordinate PML formulation is presented. It is shown that a unit step response of the ADE-CPML equations leads to a discrete form that is identical to Roden's convolutional PML method for FDTD implementations. The derivation of discrete difference operators for the ADE-CPML equations for FDTD is also presented. The ADE-CPML method is also extended in a compact form to a multiple-pole PML formulation. The advantage of the ADE-CPML method is that it provides a more flexible representation that can be extended to higher-order methods. In this paper, it is applied to the discontinuous Galerkin finite element time-domain (DGFETD) method. It is demonstrated that the ADE-CPML maintains the exponential convergence of the DGFETD method.
144 citations
TL;DR: A numerical theory based on the mixed finite element method for a time-fractional fourth-order partial differential equation (PDE) is presented and an a priori error result in H^1-norm for the scalar unknown u also is proved.
144 citations
TL;DR: In this paper, a fast implicit finite difference (FIFD) method was proposed to handle homogeneous and heterogeneous rate constants of any order of magnitude with potential steps of several millivolts.
143 citations
TL;DR: In this paper, convergence theorems for these methods are proved under various assumptions on the coupling operator, and convergence results for the stationary and evolutive versions of the mean field type models are shown.
Abstract: Mean field type models describing the limiting behavior of stochastic differential games as the number of players tends to $+\infty$ have been recently introduced by Lasry and Lions. Numerical methods for the approximation of the stationary and evolutive versions of such models have been proposed by the authors in previous works. Here, convergence theorems for these methods are proved under various assumptions on the coupling operator.
143 citations
TL;DR: In this paper, a mathematical formulation developed for aerodynamic sensitivity coefficients based on a discretized form of the compressible 2D Euler equations is presented, and a new flow prediction concept is developed and illustrated with an example.
Abstract: This study presents a mathematical formulation developed for aerodynamic sensitivity coefficients based on a discretized form of the compressible 2D Euler equations. A brief motivating introduction to the aerodynamic sensitivity analysis and the reasons behind an integrated flow/sensitivity analysis for design algorithms are presented. The finite difference approach and the quasi-analytical approach are used to determine the aerodynamic sensitivity coefficients. A new flow prediction concept, which is an outcome of the direct method in the quasi-analytical approach, is developed and illustrated with an example. Surface pressure coefficient distributions of a nozzle-afterbody configuration obtained from the predicted flowfield solution are compared successfully with their corresponding values obtained from a flowfield analysis code and the experimental data.
142 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |