  We present the MUFASA suite of cosmological hydrodynamic simulations, which
employs the GIZMO meshless finite mass (MFM) code including H2-based star
formation, nine-element chemical evolution, two-phase kinetic outflows
following scalings from the Feedback in Realistic Environments zoom
simulations, and evolving halo mass-based quenching. Our fiducial (50 Mpc/h)^3
volume is evolved to z=0 with a quarter billion particles, The predicted galaxy
stellar mass functions (GSMF) reproduce observations from z=4-0 to <1.2sigma in
cosmic variance, providing an unprecedented match to this key diagnostic. The
cosmic star formation history and stellar mass growth show general agreement
with data, with a strong archaeological downsizing trend such that dwarf
galaxies form the majority of their stars after z~1. We run 25 Mpc/h and 12.5
Mpc/h volumes to z=2 with identical feedback prescriptions, the latter
resolving all hydrogen-cooling halos, and the three runs display fair
resolution convergence. The specific star formation rates broadly agree with
data at z=0, but are underpredicted at z~2 by a factor of three, re-emphasizing
a longstanding puzzle in galaxy evolution models. We compare runs using MFM and
two flavours of Smoothed Particle Hydrodynamics, and show that the GSMF is
sensitive to hydrodynamics methodology at the ~x2 level, which is sub-dominant
to choices for parameterising feedback.
