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C. Carstensen, D. Praetorius:
"Effective Simulation of a Macroscopic Model for Stationary Micromagnetics";
Computer Methods in Applied Mechanics and Engineering, 194 (2005), 531 - 548.

The effective behaviour of stationary micromagnetic phenomena is
modelled by a convexified Landau-Lifshitz minimization problem for the
limit of large and soft magnets $\Omega$ without the exchange energy.
The numerical simulation of the resulting minimization problem has to
overcome difficulties caused by the pointwise side-restriction
$|\m|\le1$ and the stray field energy on the unbounded domain $\R^d$.
A penalty method models the side-restriction and the exterior Maxwell
equation is recast via a nonlocal integral operator $\PP$. As was
shown before, the discretization leads to a nonlocal problem with
piecewise constant ansatz and test functions and (dense) stiffness
matrices with closed form formula for their entries. This paper
addresses the numerical solution with Newton-Raphson schemes and the
scientific computation of effective micromagnetic simulations.

http://aleph.ub.tuwien.ac.at/F?base=tuw01&func=find-c&ccl_term=AC05937596

http://www.anum.tuwien.ac.at/~dirk/download/published/ccdpr03_compmeth194.pdf