101.588 VO (2std Vorlesung, Sommersemester 2015)
AKNUM: Introduction to Computational Micromagnetism
TISS-Homepage

Lecturers

When & Where

Aim of the lecture

The participants get in touch with a recent active research topic in numerical mathematics. The lecture might serve as the starting point for a diploma thesis or even a related dissertation.

Subject of the lecture

Magnetic processes play an important role in a variety of technological applications, e.g., magnetic sensors, recording heads, and magnetoresistive storage devices. On a microscale, the quantity which describes the magnetic condition of a ferromagnetic body is the magnetization, a three-dimensional vector field. In the literature, it is well accepted that the dynamics of the magnetization is governed by the Landau-Lifshitz-Gilbert equation, which describes the behavior of the magnetization under the influence of the so-called effective field, which is characterized by a multitude of physical effects. Mathematical challenges of this evolution equation are due to the strong nonlinearity, possibly complicated and nonlocal field contributions, as well as an inherent nonconvex side constraint which enforces length preservation.

In the lecture, first we introduce the theory of micromagnetism. Then, we discuss the mathematical formulation of both the stationary and the dynamical problems in micromagnetism, giving an overview of the available analytical results. Finally, we focus on the convergent numerical integrators for the LLG equation which are available in the mathematical market.

Previous knowledge

The lecture is self-contained (as much as it can be...). However, basic knowledge of the following topics might be helpful

Examination modalities

Oral examination. If you wish to do the examination, please email us to arrange an appointment.

Schedule

#DateTopicLecturer
110.03.2015Formalia, Motivation, Physical backgroundPraetorius & Ruggeri
217.03.2015Nondimensionalization, Analysis of the stray field problemRuggeri
324.03.2015Static problem in micromagnetismRuggeri
Easter holidays (Osterferien)
414.04.2015Dynamical problem in micromagnetismRuggeri
521.04.2015Finite element method (recap and extensions)Ruggeri
628.04.2015Finite element method (end of the recap), Introduction to the tangent plane schemeRuggeri
705.05.2015Analysis of the tangent plane schemeRuggeri
812.05.2015Analysis of the tangent plane scheme (continuation)Ruggeri
919.05.2015Analysis of the tangent plane scheme (continuation)Praetorius
26.05.2015: Pentecost holiday (Pfingstferien)
1002.06.2015Analysis of the tangent plane scheme (end)Ruggeri
1109.06.2015Projection-free tangent plane schemeRuggeri
16.06.2015: Vienna PDE day
1223.06.2015Midpoint scheme, Concluding remarksRuggeri

Downloads

Please email us with any corrections or comments.

19.11.2015Lectures notes (with some corrected typos)[pdf]
05.08.2015Lectures notes (final version)[pdf]
22.06.2015Lectures notes (until Section 4.1)[pdf]
02.06.2015Lectures notes (until lecture on 19.05.2015)[pdf]
27.04.2015Lectures notes (until Chapter 3)[pdf]
16.04.2015Lectures notes (Chapter 1-2 revised version + Appendix)[pdf]
14.04.2015Lectures notes (Chapter 1-2)[pdf]
19.03.2015Lectures notes (until Section 2.2)[pdf]
13.03.2015Lectures notes (Chapter 1)[pdf]