  In this paper, we address the problem that standard stochastic
Landau-Lifshitz-Gilbert (sLLG) simulations typically produce results that show
unphysical mesh-size dependence. The root cause of this problem is that the
effects of spin wave fluctuations are ignored in sLLG. We propose to represent
the effect of these fluctuations by a "FUll-Spinwave-Scaled Stochastic LLG", or
FUSSS LLG method. In FUSSS LLG, the intrinsic parameters of the sLLG
simulations are first scaled by scaling factors that integrate out the spin
wave fluctuations up to the mesh size, and the sLLG simulation is then
performed with these scaled parameters. We developed FUSSS LLG by studying the
Ferromagnetic Resonance (FMR) in Nd$_2$Fe$_{14}$B cubes. The nominal scaling
greatly reduced the mesh size dependence relative to sLLG. We further
discovered that adjusting one scaling exponent by less than 10% delivered fully
mesh-size-independent results for the FMR peak. We then performed three tests
and validations of our FUSSS LLG with this modified scaling. 1) We studied the
same FMR but with magnetostatic fields included. 2) We simulated the total
magnetization of the Nd$_2$Fe$_{14}$B cube. 3) We studied the effective,
temperature- and sweeping rate-dependent coercive field of the cubes. In all
three cases we found that FUSSS LLG delivered essentially mesh-size-independent
results, which tracked the theoretical expectations better than unscaled sLLG.
Motivated by these successful validations, we propose that FUSSS LLG provides
marked, qualitative progress towards accurate, high precision modeling of
micromagnetics in hard, permanent magnets.
