3.5 Effective Field

Finally we can collect all contributions to the effective field and calculate it by simple matrix-vector multiplications.

$$\boldsymbol{H}_{i,\mathrm{eff}} \approx -\frac{1}{V_i J_{\... ...G_\mathrm{exch}+G_\mathrm{ani})\cdot \boldsymbol{u} \right)_i$$ (3.58)

Since the matrices for the exchange and anisotropy energies depend only on the (time independent) material parameters and the geometry, they need to be calculated only once at the beginning. In order to save time and memory, they can also be assembled into a single combined matrix, if the energies and fields are not required separately.