  The magnetic geometry of the surface magnetic fields of more than 55 cool
stars have now been mapped using spectropolarimetry. In order to better
understand these observations, we compare the magnetic field topology at
different surface scale sizes of observed and simulated cool stars. For ease of
comparison between the high-resolution non-potential magnetofrictional
simulations and the relatively low-resolution observations, we filter out the
small-scale field in the simulations using a spherical harmonics decomposition.
We show that the large-scale field topologies of the solar-based simulations
produce values of poloidal/toroidal fields and fractions of energy in
axisymmetric modes that are similar to the observations. These global
non-potential evolution model simulations capture key magnetic features of the
observed solar-like stars through the processes of surface flux transport and
magnetic flux emergence. They do not, however, reproduce the magnetic field of
M-dwarfs or stars with dominantly toroidal field. Furthermore, we analyse the
magnetic field topologies of individual spherical harmonics for the simulations
and discover that the dipole is predominately poloidal, while the quadrupole
shows the highest fraction of toroidal fields. Magnetic field structures
smaller than a quadrupole display a fixed ratio between the poloidal and
toroidal magnetic energies.
