  The presence of topological defects in magnetic media often leads to normal
modes with zero frequency (zero modes). Such modes are crucial for long-time
behavior, describing, for example, the motion of a domain wall as a whole.
Conventional numerical methods to calculate the spin-wave spectrum in magnetic
media are either inefficient or they fail for systems with zero modes. We
present a new efficient computational scheme that reduces the magnetic
normal-mode problem to a generalized Hermitian eigenvalue problem also in the
presence of zero modes. We apply our scheme to several examples, including
two-dimensional domain walls and Skyrmions, and show how the effective masses
that determine the dynamics can be calculated directly. These systems highlight
the fundamental distinction between the two types of zero modes that can occur
in spin systems, which we call special and inertial zero modes. Our method is
suitable for both conservative and dissipative systems. For the latter case, we
present a perturbative scheme to take into account damping, which can also be
used to calculate dynamical susceptibilities.
