  Magnetic nanoparticles and their magnetization dynamics play an important
role in many applications. We focus on magnetization dynamics in large
ensembles of single domain nanoparticles being characterized by either Brownian
or N\'{e}el rotation mechanisms. Simulations of the respective behavior are
obtained by solving advection-diffusion equations on the sphere, for which a
unified computational framework is developed and investigated. This builds the
basis for solving two parameter identification problems, which are formulated
in the context of the chosen application, magnetic particle imaging. The
functionality of the computational framework is illustrated by numerical
results in the parameter identification problems either compared quantitatively
or qualitatively to measured data.
