An Adaptive Multigrid Solver for High-Resolution Cosmological Simulations

Abstract

We have developed an adaptive multigrid code for solving the Poisson equation in gravitational simulations. Finer rectangular subgrids are adaptively created in locations where the density exceeds a local level-dependent threshold. We describe the code, test it in cosmological simulations, and apply it to the study of the birth and evolution of a typical pancake singularity. The initial conditions for the pancake are generated on the basis of the theory of Lagrangian singularities; we follow its evolution for a few collapse times, finding a rich substructure in the final object. We achieve a spatial resolution of 1/1024 of the size of the overall computational cube in the central parts of the pancake, with computing time comparable to that of the FFT-solvers.