Accurate numerical methods for micromagnetics simulations with general geometries

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.