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F. Bruckner:
"Multiscale simulation of magnetic nanostructures";
Supervisor, Reviewer: D. Süss, D. Praetorius; Institute for Solid State Physics, 2013; oral examination: 2013-05-27.

Due to the ongoing miniaturization of modern magnetic devices, ranging from GMR sensors,
magnetic write heads, to spintronic devices, micromagnetic simulations gain more and more
importance, since they are an essential tool to understand the behavior of magnetic materials
in the nanometer scale. The use of numerical simulations allows to optimize the
microstructure of such devices or to test new concepts prior to performing expensive
experimental tests.

The purpose of this work is to extend the micromagnetic model by additional macroscopic
parts which are described in an averaged sense. In contrast to the microscopic parts which are
described by Landau-Lifshitz-Gilbert (LLG) equations, these macroscopic parts are based on
classical magnetostatic Maxwell equations, which could be extended to a full Maxwell
description in a straight-forward way. The averaged description using Maxwell equations
allows to overcome the upper bound for the discrete element sizes, which is intrinsic
to the micromagnetic models, since the detailed domain structure of the ferromagnetic
material needs to be resolved. Combining microscopic and macroscopic models and solving
the corresponding equations simultaneously provides a multiscale method, which allows to
handle problems of a dimension, which would otherwise be far out of reach. A basic
prerequisite for the application of the method, is that microscopic and macroscopic parts can
be separated into disjoint regions. The performance of the implemented algorithm is
demonstrated by the simulation of the transfer curve of a magnetic recording read head, as it
is used in current hard drives.

Independent of the former approach the use of parallelized algorithms allows to handle larger
problems. This work especially deals with the shared memory parallelization of hierarchical
matrices, since these require a large amount of the storage consumption as well as of the
computation time for typical simulations. For the setup of the matrices a nearly perfect
parallelization could be reached, whereas for the matrix-vector-multiplication the
computation time stagnates at a few computation cores, due to the restricted main memory
bandwidth.

https://repositum.tuwien.at/bitstream/20.500.12708/9970/2/Bruckner%20Florian%20-%202013%20-%20Multiscale%20simulation%20of%20magnetic%20nanostructures.pdf