Accurate Numerical Methods for Micromagnetics
Simulations with General Geometries
with Zydrunas Gimbutas and Weinan E
Abstract
In current FFT-based algorithms for micromagnetics simulations the
boundary is typically replaced by a staircase approximation along the
grid lines, either eliminating the incomplete cells or replacing them
by complete cells. Sometimes the magnetizations at the boundary cells
are weighted by the volume of the sample in the corresponding cell.
We show that this leads to large errors in the
computed exchange and stray fields. One consequence of this is that
the predicted switching mechanism
depends sensitively on the orientation of the numerical grid. We
present a boundary-corrected algorithm to efficiently and accurately
handle the incomplete cells at the boundary. We show that this
boundary-corrected algorithm greatly improves the accuracy in
micromagnetics simulations. We demonstrate by using
A. Arrott's example of a hexagonal element that the switching
mechanism is predicted independently of the grid orientation.