  Glasses show vibrational properties that are markedly different to those of
crystals which are known as phonons. For example, excess low-frequency modes
(the so-called boson peak), vibrational localization, and strong scattering of
phonons have been the most discussed topics, and a theoretical understanding of
these phenomena is challenging. To address this problem, computational
simulations are a powerful tool, which have been employed by many previous
works. In this chapter, we describe simulation methods for studying the
vibrational properties of glasses (and any solid-state materials). We first
present a method for studying vibrational eigenmodes. Since vibrational motions
of particles are excited along eigenmodes, the eigenmodes are fundamental to
descriptions of vibrational properties. The eigenmodes in glasses are
non-phonon modes in general, and some of them are even localized in space. We
next present a method of analysing phonon transport, which is also crucial for
understanding vibrational properties. Since phonons are not eigenmodes in
glasses, they are decomposed into several different, non-phonon eigenmodes. As
a result, phonons in glasses are strongly scattered. In addition, we describe
how to analyse the elastic response. The elastic response of glasses is also
anomalous with respect to that of crystals. Finally, we briefly introduce
recent advances that have been achieved by means of large-scale computational
simulations.
