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Title: The mimetic finite difference method for the Landau–Lifshitz equation

The Landau–Lifshitz equation describes the dynamics of the magnetization inside ferromagnetic materials. This equation is highly nonlinear and has a non-convex constraint (the magnitude of the magnetization is constant) which poses interesting challenges in developing numerical methods. We develop and analyze explicit and implicit mimetic finite difference schemes for this equation. These schemes work on general polytopal meshes which provide enormous flexibility to model magnetic devices with various shapes. A projection on the unit sphere is used to preserve the magnitude of the magnetization. We also provide a proof that shows the exchange energy is decreasing in certain conditions. The developed schemes are tested on general meshes that include distorted and randomized meshes. As a result, the numerical experiments include a test proposed by the National Institute of Standard and Technology and a test showing formation of domain wall structures in a thin film.
 [1] ;  [2]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of California, Berkeley, CA (United States)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Report Number(s):
Journal ID: ISSN 0021-9991
Grant/Contract Number:
AC52-06NA25396; AC05-06OR23100
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 328; Journal Issue: C; Journal ID: ISSN 0021-9991
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org:
Country of Publication:
United States
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Mathematics; micromagnetics, Landau-Lifshitz equation, mimetic finite differences, polygonal meshes
OSTI Identifier:
Alternate Identifier(s):
OSTI ID: 1397763