I published a paper a while ago, but I’ve been pretty busy so hadn’t gotten around to figuring out the rules about posting it online. Anyway it looks like I’m allowed to host it on my personal website, so here it is!

The abstract is:

```
In the numerical integration of the Landau-Lifshitz-Gilbert
(LLG) equation, stiffness (stability restrictions on the time step
size for explicit methods) is known to be a problem in some
cases. We examine the relationship between stiffness and spatial
discretisation size for the LLG with exchange and magnetostatic
effective fields. A maximum stable time step is found for the
reversal of a single domain spherical nanoparticle with a variety
of magnetic parameters and numerical methods. From the lack
of stiffness when solving a physically equivalent ODE problem
we conclude that any stability restrictions in the PDE case arise
from the spatial discretisation rather than the underlying physics.
We find that the discretisation induced stiffness increases as
the mesh is refined and as the damping parameter is decreased.
In addition we find that use of the FEM/BEM method for
magnetostatic calculations increases the stiffness. Finally, we
observe that the use of explicit magnetostatic calculations within
an otherwise implicit time integration scheme (i.e. a semi-implicit
scheme) does not cause stability issues.
```

In plain English: I investigated when and why one class of algorithms becomes more efficent than another class of algorithms for an important problem in the study of magnetic materials.

Here’s the paper itself.