Computational micromagnetism

Autor*innen

• Andreas Prohl

Parameter

• 304 Seiten
• 11 Lesestunden

• Naturwissenschaften
• Physik

Mehr zum Buch

This work examines numerical challenges related to a mathematical model for ferromagnetic materials in both stationary and non-stationary contexts, incorporating electromagnetic effects for nonstationary magneto-electronics. The latter sections focus on the numerical analysis of the Ericksen-Leslie model, which is essential for studying the fluid flow of nematic liquid crystals used in display technologies. These models share key features, including strong nonlinearities and non-convex side constraints, such as the requirement that the order parameter m satisfies |m| = 1 almost everywhere. A critical aspect of numerical modeling is ensuring that computed solutions adhere to these non-convex constraints. Various solution strategies for the variational problem of stationary micromagnetism are presented, including direct minimization, convexification, and relaxation through Young measure-valued solutions. Notably, direct minimization faces challenges due to spatial triangulation introducing artificial exchange energy contributions that can obscure relevant physical interactions. The minimizers often display complex multiple scales, particularly near the boundaries of ferromagnets, complicating efficient computation. To address this, we propose an adaptive scheme designed to better capture these intricate multiple scale structures in cubic ferromagnets.

• Sprache: Englisch
• Erscheinungsdatum: 2001
• Einband: Paperback