Classical Molecular Dynamics simulation (MD) models the interactions of thousands to millions of particles through the iterative application of basic Physics. MD is one of the core methods in High Performance Computing (HPC). While MD is critical to many high-profile applications, e.g. drug discovery and design, it suffers from the strong scaling problem, that is, while large computer systems can efficiently model large ensembles of particles, it is extremely challenging for {\it any} computer system to increase the timescale, even for small ensembles. This strong scaling problem can be mitigated with low-latency, direct communication. Of all Commercial Off the Shelf (COTS) Integrated Circuits (ICs), Field Programmable Gate Arrays (FPGAs) are the computational component uniquely applicable here: they have unmatched parallel communication capability both within the chip and externally to couple clusters of FPGAs. This thesis focuses on the acceleration of the long range (LR) force, the part of MD most difficult to scale, by using FPGAs. This thesis first optimizes LR acceleration on a single-FPGA to eliminate the amount of on-chip communication required to complete a single LR computation iteration while maintaining as much parallelism as possible. This is achieved by designing around application specific memory architectures. Doing so introduces data movement issues overcome by pipelined, toroidal-shift multiplexing (MUXing) and pipelined staggering of memory access subsets. This design is then evaluated comprehensively and comparatively, deriving equations for performance and resource consumption and drawing metrics from previously developed LR hardware designs. Using this single-FPGA LR architecture as a base, FPGA network strategies to compute the LR portion of larger sized MD problems are then theorized and analyzed.