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Numerical analysis of an explicit approximation scheme for the Landau-Lifshitz-Gilbert equation

Authors: Sören Bartels, Joy Ko and Andreas Prohl
Journal: Math. Comp. 77 (2008), 773-788
MSC (2000): Primary 65N12, 65N30, 35K55
Published electronically: October 29, 2007
MathSciNet review: 2373179
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Abstract: The Landau-Lifshitz-Gilbert equation describes magnetic behavior in ferromagnetic materials. Construction of numerical strategies to approximate weak solutions for this equation is made difficult by its top order nonlinearity and nonconvex constraint. In this paper, we discuss necessary scaling of numerical parameters and provide a refined convergence result for the scheme first proposed by Alouges and Jaisson (2006). As an application, we numerically study discrete finite time blowup in two dimensions.

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Additional Information

Sören Bartels
Affiliation: Department of Mathematics, Humboldt-Universität zu Berlin, Unter den Linden 6, D-10099 Berlin, Germany
Address at time of publication: Institut für Numerische Simulation, University of Bonn, Wegelerstr. 6, D-53115 Bonn, Germany

Joy Ko
Affiliation: Department of Mathematics, Brown University, Providence, Rhode Island 02912

Andreas Prohl
Affiliation: Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany

Received by editor(s): May 9, 2005
Received by editor(s) in revised form: November 23, 2006
Published electronically: October 29, 2007
Additional Notes: The first author was supported by Deutsche Forschungsgemeinschaft through the DFG Research Center Matheon “Mathematics for key technologies” in Berlin
The second author was partially supported by NSF grant DMS-0402788
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.