  Parallel optimizations for the 2D Hierarchical Poincar\'e-Steklov (HPS)
discretization scheme are described. HPS is a multi-domain spectral collocation
scheme that allows for combining very high order discretizations with direct
solvers, making the discretization powerful in resolving highly oscillatory
solutions to high accuracy. HPS can be viewed as a domain decomposition scheme
where the domains are connected directly through the use of a sparse direct
solver. This manuscript describes optimizations of HPS that are simple to
implement, and that leverage batched linear algebra on modern hybrid
architectures to improve the practical speed of the solver. In particular, the
manuscript demonstrates that the traditionally high cost of performing local
static condensation for discretizations involving very high local order $p$ can
be reduced dramatically.
