A comprehensive atomistic study of self-interstitial aggregation in crystalline silicon is presented. Here, large-scale parallel molecular dynamics simulations are used to generate time-dependent views into the selfinterstitial clustering process, which is important during post-implant damage annealing. The effects of temperature and pressure on the aggregation process are studied in detail and found to generate a variety of qualitatively different interstitial cluster morphologies and growth behavior. In particular, it is found that the self-interstitial aggregation process is strongly affected by hydrostatic pressure. {111}-oriented planar defects are found to be dominant under stress-free or compressive conditions while {113} rodlike and planar defects are preferred under tensile conditions. Moreover, the aggregation pathways for forming the different types of planar defect structures are found to be qualitatively different. In each case, the various cluster morphologies generated in the simulations are found to be in excellent agreement with structures previously predicted from electronic-structure calculations and observed experimentally by electron microscopy. Multiple empirical interatomic potential models were employed and found to generally provide similar results leading to a fairly consistent picture of self-interstitial aggregation. In a companion article, a detailed thermodynamic analysis of various cluster configurations is employed to probe the mechanistic origins of these observations.