9.2.2 Numerical Finite Element Simulations

A model of a cylindrical nanodot and the finite element meshes were created using the CAD software MSC/Patran. It is a very flat nanodot with a radius of $R=1$ and a height of $L=0.2$. In order to investigate the influence of the finite element mesh on the results, three meshes with different mesh density have been created (cf. Tab. 9.2).

Table 9.2: Finite element meshes of different mesh density for a circular nanodot.

	coarse mesh	fine mesh	adapted mesh
$R=1$, $L=0.2$
mesh size	0.2	0.06	0.02 to 0.4
nodes	1437	6455	1397
elements	5816	30979	6256
surface triangles	1758	5232	1390

The first mesh is a uniform tetrahedral mesh with an average mesh size of 0.2. Since the nanodot is 0.2 thick, there is only one layer of elements. The second dot has an average mesh size of 0.06, which resulted in 4 layers. The third mesh is an ``adapted'' mesh, with a very high density of nodes in the center, where the core of the vortex is found in zero external field. This is sensible, because the vortex represents a singularity, which requires a very high numerical accuracy and therefore a lot of nodes. The outer regions are meshed with larger finite elements, since the magnetization distribution is rather uniform.