The mimetic finite difference method for the Landau–Lifshitz equation

Kim, Eugenia Hail; Lipnikov, Konstantin Nikolayevich

doi:10.1016/j.jcp.2016.10.016

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

Journal Article · Sun Jan 01 00:00:00 EST 2017 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2016.10.016· OSTI ID:1331275

Kim, Eugenia Hail ^[1]; Lipnikov, Konstantin Nikolayevich ^[2]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of California, Berkeley, CA (United States)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

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.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC52-06NA25396; AC05-06OR23100

OSTI ID:: 1331275

Alternate ID(s):: OSTI ID: 1397763

Report Number(s):: LA-UR-16-21341

Journal Information:: Journal of Computational Physics, Vol. 328, Issue C; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 11 works

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Multiscale approach for magnetization dynamics: unraveling exotic magnetic states of matter Méndez, É.; Poluektov, M.; Kreiss, G. Physical Review Research, Vol. 2, Issue 1 https://doi.org/10.1103/physrevresearch.2.013092	journal	January 2020
Control of vortex chirality in bi-component magnetic nanodisks Manzin, Alessandra; Ferrero, Riccardo Applied Physics Letters, Vol. 115, Issue 4 https://doi.org/10.1063/1.5110274	journal	July 2019
A Brief Review on Polygonal/Polyhedral Finite Element Methods Perumal, Logah Mathematical Problems in Engineering, Vol. 2018 https://doi.org/10.1155/2018/5792372	journal	October 2018
A multi-scale approach for magnetisation dynamics: Unraveling exotic magnetic states of matter Méndez, É.; Poluektov, M.; Kreiss, G. arXiv https://doi.org/10.48550/arxiv.1910.07807	text	January 2019

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

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