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Efficient micromagnetic finite element simulations using a perturbed Lagrange multiplier method

Reichel, Maximilian ; Schröder, Jörg ; Xu, Bai-Xiang (2022)
Efficient micromagnetic finite element simulations using a perturbed Lagrange multiplier method.
In: PAMM - Proceedings in Applied Mathematics & Mechanics, 22 (1)
doi: 10.1002/pamm.202200016
Artikel, Bibliographie

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Kurzbeschreibung (Abstract)

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.

Typ des Eintrags: Artikel
Erschienen: 2022
Autor(en): Reichel, Maximilian ; Schröder, Jörg ; Xu, Bai-Xiang
Art des Eintrags: Bibliographie
Titel: Efficient micromagnetic finite element simulations using a perturbed Lagrange multiplier method
Sprache: Englisch
Publikationsjahr: 2022
Ort: Darmstadt
Verlag: Wiley-VCH
Titel der Zeitschrift, Zeitung oder Schriftenreihe: PAMM - Proceedings in Applied Mathematics & Mechanics
Jahrgang/Volume einer Zeitschrift: 22
(Heft-)Nummer: 1
Kollation: 6 Seiten
DOI: 10.1002/pamm.202200016
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Kurzbeschreibung (Abstract):

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.

Zusätzliche Informationen:

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

Sachgruppe der Dewey Dezimalklassifikatin (DDC): 600 Technik, Medizin, angewandte Wissenschaften > 620 Ingenieurwissenschaften und Maschinenbau
Fachbereich(e)/-gebiet(e): 11 Fachbereich Material- und Geowissenschaften
11 Fachbereich Material- und Geowissenschaften > Materialwissenschaft
11 Fachbereich Material- und Geowissenschaften > Materialwissenschaft > Fachgebiet Mechanik Funktionaler Materialien
Hinterlegungsdatum: 02 Aug 2024 12:52
Letzte Änderung: 02 Aug 2024 12:52
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