  We present a parallel computing strategy for a hybridizable discontinuous
Galerkin (HDG) nested geometric multigrid (GMG) solver. Parallel GMG solvers
require a combination of coarse-grain and fine-grain parallelism to improve
time to solution performance. In this work we focus on fine-grain parallelism.
We use Intel's second generation Xeon Phi (Knights Landing) many-core
processor. The GMG method achieves ideal convergence rates of $0.2$ or less,
for high polynomial orders. A matrix free (assembly free) technique is
exploited to save considerable memory usage and increase arithmetic intensity.
HDG enables static condensation, and due to the discontinuous nature of the
discretization, we developed a matrix vector multiply routine that does not
require any costly synchronizations or barriers. Our algorithm is able to
attain 80\% of peak bandwidth performance for higher order polynomials. This is
possible due to the data locality inherent in the HDG method. Very high
performance is realized for high order schemes, due to good arithmetic
intensity, which declines as the order is reduced.
