When a particular geometry is decided upon for simulation, this must be discretised into lots of smaller cuboidal cells to be able to use the finite difference method. Each cell is considered to be homogeneously magnetised, i.e. within a micromagnetic simulation all of the atomic magnetic moments inside this cellular domain are thought to behave as a single particle. This is an acceptable assumption because at an atomic length scale the exchange interaction, responsible for the homogeneous alignment of magnetic moments, is overwhelmingly the most significant energy term. These smaller cells can then be used to perform the simulation. The separate simulation cells represent a certain amount of magnetic material. Obviously in this instance a finer discretisation mesh  a smaller simulation cell size  is more desirable than a coarser mesh, particularly when there are curved surfaces in the geometry.

Figure 2.7 demonstrates the effect of altering the number of cells in a geometry. In the case of extremely coarse discretisation using the finite difference method, a sphere can resemble more a cuboid than a sphere (figure 2.7, left). A poor representation of the shape in the discrete model can affect the influence of the shape anisotropy (see section 2.3.2) on the magnetisation, and subsequently negatively affect the results.
Figure 2.8 shows the discretisation of a sphere using both fixed size cubic cells (finite difference) and variable sized tetrahedral cells (finite element). In this sphere example, there are four times fewer cells in the finite element example yet it is aesthetically more spherelike.
The exchange length is a length scale over which the direction of
does not change significantly, as across this length the
exchange energy is overwhelmingly the dominant component and other
influences have little effect. A coarse mesh will not allow the
software to resolve the exchange length properly, so independent
domains will not form correctly. The exchange length is calculated by
considering (Seberino and Bertram, 2001, Kronmüller and Fähnle, 2003):
The exchange length therefore gives us a quantitative measure for the required mesh resolution.

The derivation of the exchange energy in the micromagnetic theory uses the Taylor series expansion of the cosine between two moments (equation 2.19) to the secondorder. It is crucial that the maximum angle between these two adjacent moments is not high (Donahue and McMichael, 2002)  indeed if the angle becomes larger than radians, then the results of the simulation are highly inaccurate as the torque between the two spins begins to decrease when the angle is further increased; this could potentially lead to the scenario where the angle between two adjacent spins is radians  according to the secondorder Taylor expansion of the cosine, this would be a perfectly legitimate lowenergy state, although this is clearly not the case as the exchange energy and consequently the torque between these two spins in this state would be extremely large.
Incidentally, it is worth noting that since the simulation is not atomistic, (i.e. it doesn't compute the exchange energy using equation 2.2), the use of the discretised version of the micromagnetic expression for the exchange energy 2.26 is always slightly inaccurate from a quantitative perspective, however if the angle between two spins is greater than radians then the behaviour becomes qualitatively wrong.
The answer to these problems is of course to create a finer mesh; however if one makes the mesh times as fine, then the number of the cells in the simulation increases by (since the system is threedimensional) and this results in a massively increased computational overhead.