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 P3M methods. This method makes no assumptions about the local density for short range force corrections and so is consistent with the results of the P3M method in the limit that the treecode opening angle parameter, θ → 0. The PM method is parallelized using one-dimensional slice domain decomposition. Particles are distributed in slices of equal width to allow mass assignment onto mesh points. The Fourier transforms in the PM method are done in parallel using the MPI implementation of the FFTW package. Parallelization for the tree force corrections is achieved again using one-dimensional slices but the width of each slice is allowed to vary according to the amount of computational work required by the particles within each slice to achieve load balance. The tree force corrections dominate the computational load and so imbalances in the PM density assignment step do not impact the overall load balance and performance significantly. The code performance scales well to 128 processors and is significantly better than competing methods. We present preliminary results from simulations run on different platforms containing up to N = 1G particles to verify the code.