  We study the formation of planetesimals in protoplanetary disks from the
gravitational collapse of solid over-densities generated via the streaming
instability. To carry out these studies, we implement and test a particle-mesh
self-gravity module for the Athena code that enables the simulation of
aerodynamically coupled systems of gas and collisionless self-gravitating solid
particles. Upon employment of our algorithm to planetesimal formation
simulations, we find that (when a direct comparison is possible) the Athena
simulations yield predicted planetesimal properties that agree well with those
found in prior work using different numerical techniques. In particular, the
gravitational collapse of streaming-initiated clumps leads to an initial
planetesimal mass function that is well-represented by a power-law, dN/dM ~
M^{-p}, with p = 1.6 +/- 0.1, which equates to a differential size distribution
dN/dR ~ R^{-q}, with q = 2.8 +/- 0.1. We find no significant trends with
resolution from a convergence study of up to 512^3 grid zones and Npar =
1.5x10^8 particles. Likewise, the power-law slope appears indifferent to
changes in the relative strength of self-gravity and tidal shear, and to the
time when (for reasons of numerical economy) self-gravity is turned on, though
the strength of these claims is limited by small number statistics. For a
typically assumed radial distribution of minimum mass solar nebula solids
(assumed here to have dimensionless stopping time \tau = 0.3), our results
support the hypothesis that bodies on the scale of large asteroids or Kuiper
Belt Objects could have formed as the high-mass tail of a primordial
planetesimal population.
