ABSTRACT
The purpose of cosmological simulation is to describe the formation and evolution of the cosmic fluid from an almost smooth state at early epochs to the rich variety of structures observed from the present: from galaxies, clusters of galaxies, walls and sheets of galaxies to superclusters and apparently empty voids. This chapter provides a discussion on numerical methods for the gravitational N-body problem. One of the central algorithmic goals of particle methods in numerical cosmology is to integrate the orbits of N particles under their mutual gravity. The chapter reviews the linear growth of small fluctuations in an expanding background together with a description of the formation of bound structures in common cosmological models. It discusses the requirements of cosmological simulations. The chapter also discusses implementing large-N particle techniques for parallel computers and issues relevant to practical simulation.
