  Upcoming and existing large-scale surveys of galaxies require accurate
theoretical predictions of the dark matter clustering statistics for thousands
of mock galaxy catalogs. We demonstrate that this goal can be achieve with our
new Parallel Particle-Mesh (PM) Nbody code (PPM-GLAM) at a very low
computational cost. We run about 15,000 simulations with ~2 billion particles
that provide ~1% accuracy of the dark matter power spectra P(k) for
wave-numbers up to k~ 1h/Mpc. Using this large data-set we study the power
spectrum covariance matrix, the stepping stone for producing mock catalogs. In
contrast to many previous analytical and numerical results, we find that the
covariance matrix normalised to the power spectrum C(k,k')/P(k)P(k') has a
complex structure of non-diagonal components. It has an upturn at small k,
followed by a minimum at k=0.1-0.2h/Mpc. It also has a maximum at
k=0.5-0.6h/Mpc. The normalised covariance matrix strongly evolves with
redshift: C(k,k')~delta(t)^alpha P(k)P(k'), where delta is the linear growth
factor and alpha ~ 1-1.25, which indicates that the covariance matrix depends
on cosmological parameters. We also show that waves longer than 1Gpc have very
little impact on the power spectrum and covariance matrix. This significantly
reduces the computational costs and complexity of theoretical predictions:
relatively small volume ~ (1Gpc)^3 simulations capture the necessary properties
of dark matter clustering statistics. All the power spectra obtained from many
thousands of our simulations are publicly available.
