Hybridization allows numerical partial differential equations (PDEs) to be broken up into smaller problems i.e., elements, that can be solved independently and with less memory than with a single equivalent system. Methods such as matrix-free assembly can also reduce memory usage, but these methods are less flexible for anisotropic problems. In this work we provide a theoretical analysis of a hybridized, 2-D Poisson problem assembled with an summation-by-parts operator with simultaneous approximation terms (SBP-SAT). We also include an empirical evaluation of CPU implementation of the problem utilizing the PETSc library for linear algebra operations and OpenMP for parallelism. We demonstrate how the parameterization of the problem, including the num- ber of elements and the size of each element, can affect the time-to-solution by an order of magnitude.