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Temporal upscaling in micromagnetism via heterogeneous multiscale methods
École Polytechniques Fédérale de Lausanne, Switzerland.ORCID iD: 0000-0003-4481-0964
Uppsala University, Uppsala, Sweden.
Uppsala University, Uppsala, Sweden.
2019 (English)In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 345, p. 99-113Article in journal (Refereed) Published
Abstract [en]

We consider a multiscale strategy addressing the disparate scales in the Landau–Lifschitz equations in micromagnetism. At the microscopic scale, the dynamics of magnetic moments are driven by a high frequency field. On the macroscopic scale we are interested in simulating the dynamics of the magnetisation without fully resolving the microscopic scales.

The method follows the framework of heterogeneous multiscale methods and it has two main ingredients: a micro- and a macroscale model. The microscopic model is assumed to be known exactly whereas the macromodel is incomplete as it lacks effective quantities. The two models use different temporal and spatial scales and effective parameter values for the macromodel are computed on the fly, allowing for improved efficiency over traditional one-scale schemes.

For the analysis, we consider a single spin under a high frequency field and show that effective quantities can be obtained accurately with step-sizes much larger than the size of the microscopic scales required to resolve the microscopic features. Numerical results both for a single magnetic particle as well as a chain of interacting magnetic particles are given to validate the theory.

Place, publisher, year, edition, pages
2019. Vol. 345, p. 99-113
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-45332DOI: 10.1016/j.cam.2018.05.059OAI: oai:DiVA.org:mdh-45332DiVA, id: diva2:1355426
Available from: 2019-09-28 Created: 2019-09-28 Last updated: 2019-10-11Bibliographically approved

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Arjmand, Doghonay

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