  The performance of numerical micromagnetic models is limited by the
demagnetizing field computation, which typically accounts for the majority of
the computation time. For magnetization dynamics simulations explicit
evaluation methods are in common use. Higher order methods call for evaluation
of all effective field terms, including the demagnetizing field, at all
sub-steps. Here a general method of speeding up such explicit evaluation
methods is discussed, by skipping the demagnetizing field computation at
sub-steps, and instead approximating it using polynomial extrapolation based on
stored previous exact computations. This approach is tested for a large number
of explicit evaluation methods, both adaptive and fixed time-step, ranging from
2nd order up to 5th order. The polynomial approximation order should be matched
to the evaluation method order. In this case we show higher order methods with
polynomial extrapolation are more accurate than lower order methods with full
evaluation of the demagnetizing field. Moreover, for higher order methods we
show it is possible to achieve a factor of 2 or more computation speedup with
no decrease in solution accuracy.
