GOTPM: A Parallel Hybrid Particle-Mesh Treecode

We describe a parallel, cosmological N-body code based on a hybrid scheme using the particle-mesh (PM) and Barnes-Hut (BH) oct-tree algorithm. We call the algorithm GOTPM for Grid-of-Oct-Trees-Particle-Mesh. The code is parallelized using the Message Passing Interface (MPI) library and is optimized to run on Beowulf clusters as well as symmetric multi-processors. The gravitational potential is determined on a mesh using a standard PM method with particle forces determined through interpolation. The softened PM force is corrected for short range interactions using a grid of localized BH trees throughout the entire simulation volume in a completely analogous way to P$^3$M methods. This method makes no assumptions about the local density for short range force corrections and so is consistent with the results of the P$^3$M method in the limit that the treecode opening angle parameter, $\theta \to 0$. (abridged)