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
1 / 2
Papers
1 Aug 1973
TL;DR: The unimoment method as discussed by the authors decouples exterior boundary value problems from the interior boundary value problem by solving the interior problem many times so that N linearly independent solutions are generated, and the continuity conditions are then enforced by a linear combination of the N independent solutions.
Abstract: It has been shown by this investigator and numerous others [6], [7], [8] that exterior boundary value problems involving localized inhomogeneous media are most conveniently solved using finite difference or finite element techniques together with integral equations or harmonic expansions, which satisfy the radiation conditions. The methods result in large matrices that are partly full and partly sparse; and methods to solve them, such as iteration or banded matrix methods are not very satisfactory. The unimoment method alleviates the difficulties by decoupling exterior problems from the interior boundary value problems. This is done by solving the interior problem many times so that N linearly independent solutions are generated. The continuity conditions are then enforced by a linear combination of the N independent solutions, which may be done by solving much smaller matrices. Methods of generating solutions of the interior problems are discussed.
190 citations
TL;DR: This is the first proof for the stability of the ($3-\alpha$)-order scheme for the time-fractional diffusion equation and the theoretical result is validated by a number of numerical tests.
Abstract: In this paper, we consider a numerical method for the time-fractional diffusion equation. The method uses a high order finite difference method to approximate the fractional derivative in time, resulting in a time stepping scheme for the underlying equation. Then the resulting equation is discretized in space by using a spectral method based on the Legendre polynomials. The main body of this paper is devoted to carry out a rigorous analysis for the stability and convergence of the time stepping scheme. As a by-product and direct extension of our previous work, an error estimate for the spatial discretization is also provided. The key contribution of the paper is the proof of the ($3-\alpha$)-order convergence of the time scheme, where $\alpha$ is the order of the time-fractional derivative. Then the theoretical result is validated by a number of numerical tests. To the best of our knowledge, this is the first proof for the stability of the ($3-\alpha$)-order scheme for the time-fractional diffusion equation.
189 citations
TL;DR: In this paper, the authors describe the application of the finite-difference method in the time domain to the solution of 3D eigenvalue problems, where the equations are discretized in space and time, and steady state solutions are then obtained via Fourier transform.
Abstract: This paper describes the application of the finite-difference method in the time domain to the solution of three-dimensional (3-D) eigenvalue problems. Maxwell's equations are discretized in space and time, and steady-state solutions are then obtained via Fourier transform. While achieving the same accuracy and versatility as the TLM method, the finite-difference-time-domain (FD-TD) method requires less than half the CPU time and memory under identical simulation conditions. Other advantages over the TLM method include the absence of dielectric boundary errors in the treatment of 3-D inhomogeneous planar structures, such as microstrip. Some numerical results, including dispersion curves of a microstrip on anisotropic substrate, are presented.
189 citations
TL;DR: This method improves the accuracy of split-step finite difference method by introducing a compact scheme for discretization of space variable while this improvement does not reduce the stability range and does not increase the computational cost.
188 citations
26 Jun 1989
TL;DR: In this paper, the analysis of a group of three simple antennas is used to illustrate the accuracy of the FDTD (finitedifference time-domain) method and to show that various geometrical features are handled correctly by the method.
Abstract: The analysis of a group of three simple antennas is used to illustrate the accuracy of the FDTD (finite-difference time-domain) method and to show that various geometrical features are handled correctly by the method. Each antenna is a well-posed electromagnetic boundary value problem that corresponds to a realizable experimental model. The three antennas considered are of increasing complexity: an open-ended parallel plate waveguide, a cylindrical monopole, and a conical monopole. The FDTD calculations for these antennas were compared with analytical results (open-ended parallel plate waveguide) and accurate measurements in the time and frequency domains (cylindrical and conical monopoles). In all cases the agreement was excellent. >
188 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |