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University of Wales, Bangor - Mathematics Preprints 2004
Computational Applied Mathematics
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04.07 : HINES, G.V.
Simulation of the micromagnetic behaviour of
nanoelements by an adaptive wavelet method
Summary:
This thesis presents an adaptive wavelet method for the simulation
of the time evolution of the magnetization of nanoelements
and the results obtained with the numerical simulations.
The evolution of the magnetization (m)
of a nanoelement situated in a non-magnetic medium
is modelled mathematically with the Landau-Lifshitz equation.
One term in that equation, the demagnetizing field,
is derived from the solution of a Poisson equation
whose right-hand side depends on m.
Of these two equations, coupled via the magnetization,
the first one is discretized by a pointwise Euler scheme
while the other is solved with an adaptive wavelet method.
The multi-level features of wavelet bases are used to cope with
the sharp variations in the magnetization strength at the interface
between the nanoelement (where |m|=1)
and the surrounding non-magnetic region (where |m|=0),
and in the magnetization direction within the nanoelement,
which may occur under certain circumstances with the formation
of narrow domain walls.
The aim of the adaptive scheme is to make maximum use of an
affordable number of degrees of freedom by concentrating the
computational resources in the locations where the sharpest
variations in m are situated.
The challenge for such a method is to ensure that the size of
the memory and the number of operations remains proportional
to the number of degrees of freedom.
Published in:
University of Wales, Bangor, PhD thesis
(January 2004)
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