  Fast computation of demagnetization curves is essential for the computational
design of soft magnetic sensors or permanent magnet materials. We show that a
sparse preconditioner for a nonlinear conjugate gradient energy minimizer can
lead to a speed up by a factor of 3 and 7 for computing hysteresis in soft
magnetic and hard magnetic materials, respectively. As a preconditioner an
approximation of the Hessian of the Lagrangian is used, which only takes local
field terms into account. Preconditioning requires a few additional sparse
matrix vector multiplications per iteration of the nonlinear conjugate gradient
method, which is used for minimizing the energy for a given external field. The
time to solution for computing the demagnetization curve scales almost linearly
with problem size.
