  If an early matter phase of the Universe existed after inflation with the
proper power spectrum, enhanced density perturbations can decouple from the
Hubble flow, turn around and collapse. In contrast to what happens in a
radiation dominated Universe where pressure nullifies deviations from
sphericity in these perturbations, in a matter dominated Universe, the lack of
pressure although on the one hand facilitates the gravitational collapse, it
allows small deviations from sphericity to grow substantially as the collapse
takes place. The subsequent collapse is complicated: initially as non-spherical
deviations grow, the collapsing cloud takes the form of a ``Zel'dovich
pancake". After that, the more chaotic and nonlinear stage of violent
relaxation begins where shells of the cloud cross and the matter is
redistributed within a factor of a few of the free fall timescale, reaching a
spherical virialized state. During the whole process, strong gravitational
waves are emitted due to the anisotropy of the collapse and the small time
interval that the effect takes place. The emission of gravitational waves
during the stage of the violent relaxation cannot be easily estimated with an
analytical model. We perform an $N$-body simulation to capture the behaviour of
matter during this stage in order to estimate the precise spectrum of
gravitational waves produced in this scenario.
