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Efficient micromagnetic finite element simulations using a perturbed Lagrange multiplier method

Reichel, Maximilian ; Schröder, Jörg ; Xu, Bai-Xiang (2023)
Efficient micromagnetic finite element simulations using a perturbed Lagrange multiplier method.
In: PAMM - Proceedings in Applied Mathematics & Mechanics, 2022, 22 (1)
doi: 10.26083/tuprints-00023680
Article, Secondary publication, Publisher's Version

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Item Type: Article
Type of entry: Secondary publication
Title: Efficient micromagnetic finite element simulations using a perturbed Lagrange multiplier method
Language: English
Date: 12 May 2023
Place of Publication: Darmstadt
Year of primary publication: 2022
Publisher: Wiley-VCH
Journal or Publication Title: PAMM - Proceedings in Applied Mathematics & Mechanics
Volume of the journal: 22
Issue Number: 1
Collation: 6 Seiten
DOI: 10.26083/tuprints-00023680
Corresponding Links:
Origin: Secondary publication DeepGreen

High performance magnets play an important role in critical issues of modern life such as renewable energy supply, independence of fossile resource and electro mobility. The performance optimization of the established magnetic material system relies mostly on the microstructure control and modification. Here, finite element based in‐silico characterizations, as micromagnetic simulations can be used to predict the magnetization distribution on fine scales. The evolution of the magnetization vectors is described within the framework of the micromagnetic theory by the Landau‐Lifshitz‐Gilbert equation, which requires the numerically challenging preservation of the Euclidean norm of the magnetization vectors. Finite elements have proven to be particularly suitable for an accurate discretization of complex microstructures. However, when introducing the magnetization vectors in terms of a cartesian coordinate system, finite elements do not preserve their unit length a priori. Hence, additional numerical methods have to be considered to fulfill this requirement. This work introduces a perturbed Lagrangian multiplier to penalize all deviations of the magnetization vectors from the Euclidean norm in a suited manner. To reduce the resulting system of equations, an element level based condensation of the Lagrangian multiplier is presented.

Status: Publisher's Version
URN: urn:nbn:de:tuda-tuprints-236802
Additional Information:

Special Issue: 92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM)

Classification DDC: 600 Technology, medicine, applied sciences > 620 Engineering and machine engineering
Divisions: 11 Department of Materials and Earth Sciences > Material Science > Mechanics of functional Materials
Date Deposited: 12 May 2023 08:55
Last Modified: 14 Nov 2023 19:05
SWORD Depositor: Deep Green
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/23680
PPN: 509288634
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