In response to the plethora of data from current and future large-scale structure surveys of the universe, sophisticated simulations are required to obtain commensurate theoretical predictions. We have developed the Hardware/Hybrid Accelerated Cosmology Code (HACC), capable of sustained performance on powerful and architecturally diverse supercomputers to address this numerical challenge. We will investigate the numerical methods utilized to solve a problem that evolves trillions of particles, with a dynamic range of a million to one.