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I describe a nested-grid particle-mesh (NGPM) code designed to studygravitational instability in three-dimensions. The code is based upon astandard PM code. Within the parent grid I am able to define smaller sub-gridsallowing us to substantially extend the dynamical range in mass and length. Itreat the fields on the parent grid as background fields and utilize a one-wayinteractive meshing. Waves on the coarse parent grid are allowed to enter andexit the subgrid, but waves from the subgrid are precluded from effecting thedynamics of the parent grid. On the parent grid the potential is computed usinga standard multiple Fourier transform technique. On the subgrid I use a Fouriertransform technique to compute the subgrid potential at high resolution. Iimpose quasi-isolated boundary conditions on the subgrid using the standardmethod for generating isolated boundary conditions, but rather than using theisolated Green function I use the Ewald method to compute a Green function onthe subgrid which possesses the full periodicity of the parent grid. I presenta detailed discussion of my methodology and a series of code tests.Comment: 13 pages, 10 figures included, uses mn.sty & epsf.sty. Accepted by  MNRAS. This is the final refereed versio

A nested-grid particle-mesh code for high-resolution simulations of gravitational instability in cosmology