  We present high-resolution computer simulations of dust dynamics and
planetesimal formation in turbulence generated by the magnetorotational
instability. We show that the turbulent viscosity associated with
magnetorotational turbulence in a non-stratified shearing box increases when
going from 256^3 to 512^3 grid points in the presence of a weak imposed
magnetic field, yielding a turbulent viscosity of $\alpha\approx0.003$ at high
resolution. Particles representing approximately meter-sized boulders
concentrate in large-scale high-pressure regions in the simulation box. The
appearance of zonal flows and particle concentration in pressure bumps is
relatively similar at moderate (256^3) and high (512^3) resolution. In the
moderate-resolution simulation we activate particle self-gravity at a time when
there is little particle concentration, in contrast with previous simulations
where particle self-gravity was activated during a concentration event. We
observe that bound clumps form over the next ten orbits, with initial birth
masses of a few times the dwarf planet Ceres. At high resolution we activate
self-gravity during a particle concentration event, leading to a burst of
planetesimal formation, with clump masses ranging from a significant fraction
of to several times the mass of Ceres. We present a new domain decomposition
algorithm for particle-mesh schemes. Particles are spread evenly among the
processors and the local gas velocity field and assigned drag forces are
exchanged between a domain-decomposed mesh and discrete blocks of particles. We
obtain good load balancing on up to 4096 cores even in simulations where
particles sediment to the mid-plane and concentrate in pressure bumps.
