Goldenits, P., Praetorius, D., & Süss, D. (2011). Convergent Geometric Integrator for the Landau-Lifshitz-Gilbert Equation in Micromagnetics. Proceedings in Applied Mathematics and Mechanics, 11(1), 775–776. https://doi.org/10.1002/pamm.201110376
E138-03 - Forschungsbereich Functional and Magnetic Materials E101-02 - Forschungsbereich Numerik
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Journal:
Proceedings in Applied Mathematics and Mechanics
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Date (published):
Dec-2011
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Number of Pages:
2
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Publisher:
Wiley, 11
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Peer reviewed:
No
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Keywords:
FEM; Landau-Lifshitz-Gilbert Equation; Time Integration; nonlinear; nonconvex
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Abstract:
We consider a finite element scheme of lowest order for the Landau-Lifshitz-Gilbert equation (LLG) which describes the dynamics of micromagnetism. In contrast to previous works, we examine LLG including the total magnetic field induced by several physical phenomena described in terms of exchange energy, anisotropy energy, magnetostatic energy, and Zeeman energy. Besides a strong nonlinearity and a non-convex side constraint, the non-local dependence of the demagnetization field from the magnetization represents a challenging task for the numerical integrator. Nevertheless, we prove unconditional convergence for the approximation of a weak solution.
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Research Areas:
Mathematical and Algorithmic Foundations: 75% Computational Materials Science: 25%
