Accuracy of the analytical demagnetization tensor for various geometries

We investigate the accuracy of the analytical expressions for the magnetostatic demagnetization tensor for three different geometries by comparing these to the dipole field at far-away distances. We consider a prism, tetrahedron and cylindrical tile geometry. We show that for the prism and tetrahedron tiles the median relative error compared to the dipole field reaches below 10⁻⁷ at 200 tile radii away from the generating tile, while the cylindrical tile has a median relative error of about 10⁻⁵ at this distance. Even at a distance of 10⁴ tile radii the relative error is below 10⁻² for all tiles, also when single precision is used to calculate the magnetic field. This shows that the demagnetization tensor is an accurate way of calculating the stray magnetic field also for far-away distances.