We present a GPU-accelerated global registration method for registering partial shapes, a common and often performance-critical task in many robotics, vision, and graphics applications. Global registration based on descriptor matching is highly dependent on the quality at which a shape is sampled, and computing expressive descriptors typically incurs high computation time. In this paper, we augment a global pair-wise registration algorithm based on hierarchical shape descriptors with a GPU-accelerated descriptor construction process, reducing the time spent on building descriptors by an order of magnitude. This allows for building more expressive descriptors, achieving a dual gain in both performance and accuracy. We conducted extensive evaluations on a large set of pair-wise registration problems, demonstrating very competitive registration accuracy, often rendering subsequent refinement with a local method unnecessary.