An Adaptive Multigrid Solver for High-Resolution Cosmological Simulations

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.