  We present a computer code written in C that is designed to simulate
structure formation from collisionless matter. The code is purely grid-based
and uses a recursively refined Cartesian grid to solve Poisson's equation for
the potential, rather than obtaining the potential from a Green's function.
Refinements can have arbitrary shapes and in practice closely follow the
complex morphology of the density field that evolves. The timestep shortens by
a factor two with each successive refinement. It is argued that an appropriate
choice of softening length is of great importance and that the softening should
be at all points an appropriate multiple of the local inter-particle
separation. Unlike tree and P3M codes, multigrid codes automatically satisfy
this requirement. We show that at early times and low densities in cosmological
simulations, the softening needs to be significantly smaller relative to the
inter-particle separation than in virialized regions. Tests of the ability of
the code's Poisson solver to recover the gravitational fields of both
virialized halos and Zel'dovich waves are presented, as are tests of the code's
ability to reproduce analytic solutions for plane-wave evolution. The times
required to conduct a LCDM cosmological simulation for various configurations
are compared with the times required to complete the same simulation with the
ART, AP3M and GADGET codes. The power spectra, halo mass functions and
halo-halo correlation functions of simulations conducted with different codes
are compared.
