  Following our previous work, we continue to explore gravitational dark matter
production during the minimal preheating caused by inflaton self-resonance. In
this situation there is only one dimensionless index parameter $n$
characterizing the inflation potential after the end of inflation, which leads
to a robust prediction on the gravitational dark matter relic abundance. Using
lattice method to handle the non-perturbative evolutions of relevant quantities
during the inflaton self-resonance, we derive the gravitational dark matter
relic abundance arising from both the inflaton condensate and fluctuation
annihilation. While being absent for $n=2$, the former one can instead dominate
over the later one for $n=4,6$. Our results show that gravitational dark matter
mass of $1.04~(2.66)\times 10^{14}$ GeV accommodates the observed value of dark
matter relic abundance for $n=4$ (6).
