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A spin dynamics simulation approach is proposed which is very much faster than a conventional ab initio spin dynamics code but which-nevertheless-exhibits ab initio or near-ab initio accuracy. In this approach the anewed ab initio calculation of the effective fields acting on the various spins in each time step of the spin dynamics algorithm which is required in the conventional ab initio codes and which makes them very costly is avoided. Instead, before starting the simulation, an analytical parametrization of the adiabatic energy hypersurface E for arbitrary spin orientations is obtained via the recently developed spin cluster expansion, and then the effective fields can be determined by simple derivatives. The new approach makes it possible to investigate the spin dynamics of technologically interesting spin nanostructures with strong atomic scale spin inhomogeneities like spin vortices. (C) 2004 Elsevier B.V. All rights reserved.