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
TL;DR: In this paper, a method for computing the modes of dielectric guiding structures based on finite differences is described, and the numerical computation program is efficient and can be applied to a wide range of problems.
Abstract: A method for computing the modes of dielectric guiding structures based on finite differences is described. The numerical computation program is efficient and can be applied to a wide range of problems. We report here solutions for circular and rectangular dielectric waveguides and compare our solutions with those obtained by other methods. Limitations in the commonly used approximate formulas developed by Marcatili are discussed.
120 citations
17 May 1998
TL;DR: In this article, the effect of the boundary condition representation and the introduced errors on temperature response at the heat source is studied, particularly for large surges of a short time duration, and an analytic model developed by applying an internal approximation of the heat diffusion problem is developed.
Abstract: The literature proposes some thermal models needed for the electrothermal simulation of power electronic systems. This paper gives a useful analysis about the choice of the thermal model circuit networks, equivalent to a discretization of the heat equation by the finite difference method (FDM) and the finite-element method (FEM), and an analytic model developed by applying an internal approximation of the heat diffusion problem. The effect of the boundary condition representation and the introduced errors on temperature response at the heat source are studied. This study is advantageous, particularly for large surges of a short time duration.
120 citations
TL;DR: This paper proves the convergence of the ghost fluid method for second order elliptic partial differential equations with interfacial jumps through discretization of the weak formulation of the problem.
Abstract: This paper proves the convergence of the ghost fluid method for second order elliptic partial differential equations with interfacial jumps. A weak formulation of the problem is first presented, which then yields the existence and uniqueness of a solution to the problem by classical methods. It is shown that the application of the ghost fluid method by Fedkiw, Kang, and Liu to this problem can be obtained in a natural way through discretization of the weak formulation. An abstract framework is given for proving the convergence of finite difference methods derived from a weak problem, and as a consequence, the ghost fluid method is proved to be convergent.
119 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |