The interaction between droplets and solid surfaces is of great importance in industrial applications, biochemical processes, and fundamental materials research on surface wettability. In this work, a three-dimensional spectral boundary element method has been employed to investigate the dynamics of a viscous droplet moving under gravity influence normal and parallel to a micro-patterned solid surface. The dynamics of the droplet moving perpendicular to the substrate are investigated under the influence of Bond number, droplet size, and topological features of the substrate. We find that the droplet dynamics can be controlled by varying Bond number, droplet size, and pattern height and width; however, the pattern length has little effect. For a droplet moving parallel to the surface, the Bond number and pattern projection direction greatly change the droplet dynamics. However, after moving past the pattern, the droplet position, velocity, and deformation return to that of a flat-plate solution.