A new hierachical particle-mesh code for very large scale cosmological N-body simulations

We describe a new hierarchical particle-mesh three-dimensional N-body code (HPM) for the gravitational evolution of structure in the expanding universe. The basis of the code is a standard particle-mesh (PM) code, where Poisson's equation is solved on a cubical grid with fast Fourier transform techniques and periodic boundary conditions. In a cube we can put several subgrids which themselves can have subgrids, and so forth. In these subgrids we solve for self-gravity with isolated boundary conditions at higher resolution on a cubical grid with the same techniques as before. The fields from the father grid and its father grid, and so on, are treated as external flelds. There is no back-reaction to father grids, and particles can enter and exit subgrids. With this scheme we increase dramatically the dynamic range in length and mass compared to a standard PM code. In a four-grid code the dynamic range can be extended to 6000 in length and 11 orders of magnitude in mass. The initial conditions are generated with a random phase realization of the power spectrum of the growing mode using the Zel'dovich approximation. This code is significantly faster than tree codes and particle-particle-particle-mesh (PPPM) codes, and it has a much larger dynamic range in mass than these codes. The penalty is that only a small part of space is treated at high resolution. We discuss comparisons with other codes and present tests of the code both in linear and nonlinear regimes. This code is most useful in situations where large dynamic range is important.