A finite element based heterogeneous multiscale method for the Landau-Lifshitz equation

We present a Heterogeneous Multiscale Method for the Landau-Lifshitz equation with a highly oscillatory diffusion coefficient, a simple model for a ferromagnetic composite. A finite element macro scheme is combined with a finite difference micro model to approximate the effective equation correspond...

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Bibliographic Details
Published in:	Journal of computational physics Vol. 486; p. 112112
Main Authors:	Leitenmaier, Lena, Nazarov, Murtazo
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01.08.2023
Subjects:	Beräkningsvetenskap med inriktning mot numerisk analys Finite element method Heterogeneous Multiscale Methods Micromagnetics Scientific Computing with specialization in Numerical Analysis Finite element method Micromagnetics Heterogeneous Multiscale Methods
ISSN:	0021-9991, 1090-2716, 1090-2716
Online Access:	Get full text
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Summary:	We present a Heterogeneous Multiscale Method for the Landau-Lifshitz equation with a highly oscillatory diffusion coefficient, a simple model for a ferromagnetic composite. A finite element macro scheme is combined with a finite difference micro model to approximate the effective equation corresponding to the original problem. This makes it possible to obtain effective solutions to problems with rapid material variations on a small scale, described by ε≪1, which would be too expensive to resolve in a conventional simulation. •Numerical homogenization using Heterogeneous Multiscale Methods.•Implementation of a new multiscale approach for the Landau-Lifshitz equation.•Finite element discretized macro model for flexibility.•Efficient finite difference micro model.•Makes it possible to treat arbitrarily small material variations.
ISSN:	0021-9991 1090-2716 1090-2716
DOI:	10.1016/j.jcp.2023.112112