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A Comparison of Three Time-stepping Methods for the LLG Equation in Dynamic Micromagnetics
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing.
2017 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

Micromagnetism is the study of magnetic materials on the microscopic length scale (of nano to micrometers), this scale does not take quantum mechanical effects into account, but is small enough to neglect certain macroscopic effects of magnetism in a material.

The Landau-Lifshitz-Gilbert (LLG) equation is used within micromagnetism to determine the time evolution of the magnetisation vector field in a ferromagnetic solid. It is a partial differential equation with high non linearity, which makes it very difficult so solve analytically. Thus numerical methods have been developed for approximating the solution using computers.

In this report we compare the performance of three different numerical methods for the LLG equation, the implicit midpoint method (IMP), the midpoint with extrapolation method (MPE), and the Gauss-Seidel Projection method (GSPM).

It was found that all methods have convergence rates as expected; second order for IMP and MPE, and first order for GSPM. Energy conserving properties of the schemes were analysed and neither MPE or GSPM conserve energy. The computational time required for each method was determined to be very large for the IMP method in comparison to the other two. Suggestions for different areas of use for each method are provided.

Place, publisher, year, edition, pages
2017. , 20 p.
Series
TVE, TVE-F 17 005 maj
Keyword [en]
LLG equation, Micromagnetism, Implicit midpoint, Midpoint extrapolation, Projection method
National Category
Other Computer and Information Science Computational Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-323537OAI: oai:DiVA.org:uu-323537DiVA: diva2:1106589
Educational program
Master Programme in Engineering Physics
Supervisors
Examiners
Available from: 2017-07-06 Created: 2017-06-07 Last updated: 2017-07-06Bibliographically approved

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Other Computer and Information ScienceComputational Mathematics

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CiteExportLink to record
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