Computing the forces derived from long-range electrostaticsis a critical application and also a central part of MolecularDynamics. Part of that computation, the transformation of a charge grid to a potential grid via a 3D FFT, has received some attentionrecently and has been found to work extremely well on FPGAs. Here we report on the rest of the computation, which consists oftwo mappings: charges onto a grid and a potential grid onto theparticles. These mappings are interesting in their own right as theyare far more compute intensive than the FFTs, each is typicallydone using tricubic interpolation. We believe that these mappingshave been studied only once previously for FPGAs and then foundto be exorbitantly expensive, i.e., only bicubic would fit on the chip. In the current work we find that, when using the Altera Arria 10, not only do both mappings fit, but also an appropriately sized 3DFFT. This enables the building of a balanced accelerator for theentire long-range electrostatics computation on a single FPGA. Thisdesign scales directly to FPGA clusters. Other contributions include a new mapping scheme based on table lookup and a measure of the utility of the floating point support of the Arria-10.