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 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 epsilon << 1, which would be too expensive to resolve in a conventional simulation. (c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

We propose a Heterogeneous Multiscale Method for the Landau-Lifshitz equation with a highly oscillatory diffusion coefficient, which serves as a simple model for a ferromagnetic composite. The combination of a finite element macro scheme and a finite difference micro model enables us to approximate the effective equation corresponding to the original problem. This method allows us to obtain efficient solutions for problems with rapid material variations on a small scale, described by epsilon << 1, which would be too costly to resolve in a conventional simulation.