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
15 Dec 2007
TL;DR: In this article, finite difference methods are applied to numerical micromagnetics in two variants for the description of both exchange interactions/boundary conditions and demagnetizing field evaluation.
Abstract: Micromagnetics is based on the one hand on a continuum approximation of exchange interactions, including boundary conditions, on the other hand on Maxwell equations in the nonpropagative (static) limit for the evaluation of the demagnetizing field. The micromagnetic energy is most often restricted to the sum of the exchange, demagnetizing or self-magnetostatic, Zeeman, and anisotropy energies. When supplemented with a time evolution equation, including field induced magnetization precession, damping and possibly additional torque sources, micromagnetics allows for a precise description of magnetization distributions within finite bodies both in space and time. Analytical solutions are, however, rarely available. Numerical micromagnetics enables the exploration of complexity in small size magnetic bodies. Finite difference methods are here applied to numerical micromagnetics in two variants for the description of both exchange interactions/boundary conditions and demagnetizing field evaluation. Accuracy in the time domain is also discussed and a simple tool provided in order to monitor time integration accuracy. A specific example involving large angle precession, domain wall motion as well as vortex/antivortex creation and annihilation allows for a fine comparison between two discretization schemes with as a net result, the necessity for mesh sizes well below the exchange length in order to reach adequate convergence.
Keywords:
micromagnetics;
finite differences;
boundary conditions;
Landau—Lifshitz—Gilbert;
magnetization dynamics;
approximation order
105 citations
1 Jan 1994
TL;DR: In this article, a method of finite differences is used to solve the forward problem for a given piston configuration; some nontrivial issues arise in determining boundary conditions, and the finite difference equations are then rearranged into a linear system of equations which formulates the inverse problem.
Abstract: In elasticity imaging, a surface deformation is applied to an object using small pistons, and the resulting induced strains in the interior of the object are measured using ultrasonic imaging. Two important problems are considered: (1) the forward problem of determining the strains induced by a known deformation of an object with known elasticity; and (2) the inverse problem of reconstructing elasticity from measured strains and the equations of equilibrium. The method of finite differences is used to solve the forward problem for a given piston configuration; some nontrivial issues arise in determining boundary conditions. The finite difference equations are then rearranged into a linear system of equations which formulates the inverse problem; this system can be solved for the unknown elasticities. This formulation of the inverse problem is completely consistent with the forward problem; this is useful for iterative methods in which the deformation is adaptively changed. A comparison between simulated and actual measured results demonstrate the feasibility of the proposed procedure. >
105 citations
TL;DR: In this paper, the authors discuss the derivation and use of local pressure boundary conditions for finite difference schemes for the unsteady incompressible Navier?Stokes equations in the velocity?pressure formulation.
105 citations
TL;DR: A Lagrangian-Eulerian method with zoomable hidden fine-mesh approach (LEZOOM) is used to solve the advection-dispersion equation as mentioned in this paper.
Abstract: A Lagrangian-Eulerian method with zoomable hidden fine-mesh approach (LEZOOM), that can be adapted with either finite element or finite difference methods, is used to solve the advection-dispersion equation. The approach is based on automatic adaptation of zooming a hidden fine mesh in regions where the sharp front is located. Application of LEZOOM to four bench mark problems indicates that it can handle the advection-dispersion/diffusion problems with mesh Peclet numbers ranged from 0 to {infinity} and with mesh Courant numbers well in excess of 1. Difficulties that can be resolved with LEZOOM include numerical dispersion, oscillations, the clipping of peaks, and the effect of grid orientation. Nonuniform grid as well as spatial temporally variable flow pose no problems with LEZOOM. Both initial and boundary value problems can be solved accurately with LEZOOM. It is shown that although the mixed Lagrangian-Eulerian (LE) approach (LEZOOM without zooming) also produces excessive numerical dispersion as the upstream finite element (UFE) method, the LE approach is superior to the UFE method.
104 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |