An adaptive hierarchical particle-mesh code with isolated boundary   conditions
  This article describes a new, fully adaptive Particle-Multiple-Mesh numerical simulation code developed primarily for simulations of small regions (such as a group of galaxies) in a cosmological context. It integrates the equations of motion of a set of particles subject to their mutual gravitational interaction and to an arbitrary external field. The interactions are computed using a hierarchy of nested grids constructed anew at each integration step to enhance the spatial resolution in high-density regions of interest. Significant effort has gone into supporting isolated boundary conditions at the top grid level. This makes our method also applicable to non-cosmological problems, at the cost of some complications which we discuss. We point out the implications of some differences between our approach and those of other authors of similar codes, in particular with respect to the handling of the interface between regions of different spatial resolution. We present a selection of tests performed to verify the correctness and performance of our implementation. The conclusion suggests possible further improvements in the areas of independent time steps and particle softening lengths. 
Sergio Gelato, David F. Chernoff, Ira Wasserman