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

Bartels, Sören; Ko, Joy; Prohl, Andreas

doi:10.1090/S0025-5718-07-02079-0

Numerical analysis of an explicit approximation scheme for the Landau-Lifshitz-Gilbert equation
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by Sören Bartels, Joy Ko and Andreas Prohl PDF

Math. Comp. 77 (2008), 773-788 Request permission

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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