  We present efficient numerical methods for the simulation of small
magnetization oscillations in three-dimensional micromagnetic systems.
Magnetization dynamics is described by the Landau-Lifshitz-Gilbert (LLG)
equation, linearized in the frequency domain around a generic equilibrium
configuration, and formulated in a special operator form that allows leveraging
large-scale techniques commonly used to evaluate the effective field in
time-domain micromagnetic simulations. By using this formulation, we derive
numerical algorithms to compute the free magnetization oscillations (i.e., spin
wave eigenmodes) as well as magnetization oscillations driven by ac
radio-frequency fields for arbitrarily shaped nanomagnets. Moreover,
semi-analytical perturbation techniques based on the computation of a reduced
set of eigenmodes are provided for fast evaluation of magnetization frequency
response and absorption spectra as a function of damping and ac field. We
present both finite difference and finite element implementations and
demonstrate their effectiveness on a test case. These techniques open the
possibility to study generic magnonic systems discretized with several hundred
thousand (or even millions) of computational cells in a reasonably short time.
