  The past decade has witnessed a dramatic acceleration of lattice quantum
chromodynamics calculations in nuclear and particle physics. This has been due
to both significant progress in accelerating the iterative linear solvers using
multi-grid algorithms, and due to the throughput improvements brought by GPUs.
Deploying hierarchical algorithms optimally on GPUs is non-trivial owing to the
lack of parallelism on the coarse grids, and as such, these advances have not
proved multiplicative. Using the QUDA library, we demonstrate that by exposing
all sources of parallelism that the underlying stencil problem possesses, and
through appropriate mapping of this parallelism to the GPU architecture, we can
achieve high efficiency even for the coarsest of grids. Results are presented
for the Wilson-Clover discretization, where we demonstrate up to 10x speedup
over present state-of-the-art GPU-accelerated methods on Titan. Finally, we
look to the future, and consider the software implications of our findings.
