The complex theology of colloidal suspensions under shear flows is a direct consequence of shear-induced microstructural changes. Non-equilibrium Brownian Dynamics (NEED) simulations can be used to study and understand this theology and its relationship to the suspension microstructure. However, system size effects can influence the observed theology and structural evolution. In this paper, we describe a data parallel algorithm for NEED appropriate for a SIMD architecture and apply it to simulate systems of >250,000 Brownian disks under simple shear. The evolution of the shear and normal stesses is explained by detailed examination of the shear-induced microstructure. A transition to a string phase is seen consistent with experiments and smaller simulations, showing it not to be an artifact of simulation size effects.