# 101.588 VO (2std Vorlesung, Sommersemester 2015)

AKNUM: Introduction to Computational Micromagnetism

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## Lecturers

## When & Where

- Tuesday, 09:15-10:45
- Seminarraum 101B (green section, 3rd floor)
- First lecture:
**Tuesday, 10.03.2015**

## 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

- numerical methods for PDEs (in particular, finite element methods)
- classical results of functional analysis
- analysis of PDEs

## Examination modalities

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

## Schedule

# | Date | Topic | Lecturer |
---|---|---|---|

1 | 10.03.2015 | Formalia, Motivation, Physical background | Praetorius & Ruggeri |

2 | 17.03.2015 | Nondimensionalization, Analysis of the stray field problem | Ruggeri |

3 | 24.03.2015 | Static problem in micromagnetism | Ruggeri |

Easter holidays (Osterferien) | |||

4 | 14.04.2015 | Dynamical problem in micromagnetism | Ruggeri |

5 | 21.04.2015 | Finite element method (recap and extensions) | Ruggeri |

6 | 28.04.2015 | Finite element method (end of the recap), Introduction to the tangent plane scheme | Ruggeri |

7 | 05.05.2015 | Analysis of the tangent plane scheme | Ruggeri |

8 | 12.05.2015 | Analysis of the tangent plane scheme (continuation) | Ruggeri |

9 | 19.05.2015 | Analysis of the tangent plane scheme (continuation) | Praetorius |

26.05.2015: Pentecost holiday (Pfingstferien) | |||

10 | 02.06.2015 | Analysis of the tangent plane scheme (end) | Ruggeri |

11 | 09.06.2015 | Projection-free tangent plane scheme | Ruggeri |

16.06.2015: Vienna PDE day | |||

12 | 23.06.2015 | Midpoint scheme, Concluding remarks | Ruggeri |

## Downloads

Please email us with any corrections or comments.

19.11.2015 | Lectures notes (with some corrected typos) | [pdf] |

05.08.2015 | Lectures notes (final version) | [pdf] |

22.06.2015 | Lectures notes (until Section 4.1) | [pdf] |

02.06.2015 | Lectures notes (until lecture on 19.05.2015) | [pdf] |

27.04.2015 | Lectures notes (until Chapter 3) | [pdf] |

16.04.2015 | Lectures notes (Chapter 1-2 revised version + Appendix) | [pdf] |

14.04.2015 | Lectures notes (Chapter 1-2) | [pdf] |

19.03.2015 | Lectures notes (until Section 2.2) | [pdf] |

13.03.2015 | Lectures notes (Chapter 1) | [pdf] |