A Gauss-Seidel Projection Method for Micromagnetics Simulations
with Xiao-Ping Wang and Weinan E
Abstract
One of the main difficulties in micromagnetics simulations is
the severe time step constraint introduced by the exchange
field. Using standard explicit integrators leads to a physical
time step of sub-pico seconds, which is often two orders of magnitude
smaller than the fastest physical time scales. Direct implicit
integrators require
solving complicated, coupled systems. In this paper, we
introduce an implicit method whose complexity is comparable to solving
the scalar heat equation implicitly. This method is based on a
combination of a Gauss-Seidel implementation of a fractional-step
implicit solver for the gyromagnetic term, and the projection method
for the heat flow of harmonic maps. This method allows us to carry out
fully resolved calculations for the switching of the magnetization in
micron-sized elements.