Finite difference

About: Finite difference is a research topic. Over the lifetime, 19693 publications have been published within this topic receiving 408603 citations.

Possibilities of finite calculus in computational mechanics

Abstract: The expression “finite calculus” refers to the derivation of the governing differential equations in mechanics by invoking balance of fluxes, forces, etc. in a domain of finite size. The governing equations resulting from this approach are different from those of infinitessimal calculus theory and they incorporate new terms depending on the dimensions of the balance domain. The new modified equations allow to derive naturally stabilized numerical schemes using finite element, finite difference, finite volume or meshless methods. The paper briefly discusses the possibilities of the modified governing equations derived via the finite calculus technique for the numerical solution of convection-diffusion problems, incompressible flow and incompressible solid mechanic problems and strain localization problems.

A Finite Difference Delay Modeling Approach to the Discretization of the Time Domain Integral Equations of Electromagnetics

Abstract: A new method for solving the time-domain integral equations of electromagnetic scattering from conductors is introduced. This method, called finite difference delay modeling, appears to be completely stable and accurate when applied to arbitrary structures. The temporal discretization used is based on finite differences. Specifically, based on a mapping from the Laplace domain to the z-transform domain, first- and second-order unconditionally stable methods are derived. Spatial convergence is achieved using the higher-order divergence-conforming vector bases of Graglia et al. Low frequency instability problems are avoided with the loop-tree decomposition approach. Numerical results will illustrate the accuracy and stability of the technique.

Numerical Simulations of Large Water Waves due to Landslides

Abstract: A mathematical model based on the hydrodynamic shallow water equations is developed for numerical simulation of slide generated waves in fjords. The equations are solved numerically by a finite difference technique. To examine the performance of the numerical model we have simulated the slide catastrophe in Tafjord, western Norway, 1934. The predicted runup heights are in good agreement with measured runup heights. The effects of wave amplification are estimated in runup zones with gentle beach slopes. The model results reveal wave energy trapping due to the fjord geometry. This causes standing wave oscillations in accordance with the observations.

The finite difference algorithm for higher order supersymmetry

Abstract: The higher order supersymmetric partners of the Schroedinger's Hamiltonians can be explicitly constructed by iterating a simple finite difference equation corresponding to the Baecklund transformation. The method can completely replace the Crum determinants. Its limiting, differential case offers some new operational advantages.