428 Numerical simulations in cosmology
Figure 15.1. An example of the construction of mass refinement in real space (top)
and in phase space (bottom). In real space (top panel) three central blocks of particles
were marked for highest mass resolution. Each block produces 16^2 of smallest particles.
Adjacent blocks get one step lower resolution and produce 8^2 particles each. The procedure
is repeated recursively. In phase space (bottom panel) small points in the left-hand
bottom corner represent the harmonics used for the low-resolution simulation. For the
high-resolution run with box ratios 1:1/8:1/16 the phase space is sampled more coarsely,
but high frequencies are included. Each harmonic (different markers) represents a small
cube of the phase space indicated by squares. In this case the matching of the harmonics is
not perfect: there are overlapping blocks and gaps. In any case, the waves inside domains
A and B are missed in the simulation.