# 101.847 AKANW-AKMOD-AKNUM The mathematics of magnetic materials This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_20",{id:"j_id_20",showEffect:"fade",hideEffect:"fade",target:"isAllSteop"});});This course is in at least 1 assigned curriculum part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_22",{id:"j_id_22",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});}); 2020S

2020S, VO, 2.0h, 3.0EC, to be held in blocked form

## Properties

• Semester hours: 2.0
• Credits: 3.0
• Type: VO Lecture

## Learning outcomes

After successful completion of the course, students are able to understand some mathematical models of magnetic materials, which involve nonlinear partial differential equations (PDEs), nonlocal effects, nonconvex energies and constraints. The analytical and numerical techniques presented in the lecture can be applied to treat other mathematical models.

## Subject of course

Magnetic phenomena have been known for millennia, since in ancient times people noticed that lodestones (magnetite) could attract iron. Nowadays, the use of magnetic materials in technological processes is ubiquitous (e.g., energy transformation and data storage). Moreover, they play an essential role in many devices (e.g., magnetic sensors and actuators, electric motors and generators, microphones, loudspeakers, telephones, and hard disk drives).

Magnetic processes are multiscale and multiphysics phenomena and their modeling involves nonlinear partial differential equations (PDEs), nonlocal effects, nonconvex energies and constraints.

In this lecture, we give an overview on the mathematics behind magnetic materials, touching on several topics, mostly in the fields of mathematical modeling, analysis, and numerics.

Topics and keywords:

• Modeling: magnetic moment, type of magnetism, atomistic vs. continuum theories, micromagnetics, hysteresis, Maxwell equations, Landau-Lifshitz-Gilbert (LLG) equations.
• Analysis: micromagnetic energy minimization, thin-film limits, existence and (non)uniqueness results for LLG equations.
• Numerics: numerical treatment of Maxwell and LLG equations, finite element methods, boundary element methods, unconditional stability and convergence.

Further topics could be also addressed depending on students' interests.

## Teaching methods

Blackboard and beamer presentations given by the lecturer.

## Mode of examination

Oral

The participants get in touch with active research topics in applied mathematics. The lecture can serve as the starting point for a diploma thesis or even a related dissertation.

## Course dates

DayTimeDateLocationDescription
Tue13:00 - 14:0003.03.2020Sem.R. DA grün 04 First meeting
Mon11:00 - 13:0009.03.2020Sem.R. DA grün 04 Lecture
Course is held blocked

## Examination modalities

Oral exam about the content of the lecture.

Not necessary

## Literature

The lecture notes will be assembled on-the-fly and will be published on the lecture's webpage.

## Previous knowledge

The lecture will be self-contained (as much as it can be...). However, basic knowledge in calculus of variations and (numerical) analysis of PDEs can be helpful.

## Language

if required in English