That sounds just like Particle Mesh Ewald, which we use in molecular dynamics to approximate the forces of pairwise interactions (interpolated on a grid). Ihttps://en.wikipedia.org/wiki/P3M
It's similar but I worked on magnetic spin systems with dipole-dipole interactions, so there wasn't the interpolation part, and as I understand it in Ewald summation you're always assuming periodic boundary conditions.
In our spin systems you basically pre-compute the interaction kernel tensor and can either take into account periodicity or ignore it depending on what sort of system you're looking at. Often you don't want the periodic effect since the dipole-dipole interaction is only one of many, much of the interesting phenomena in magnetics is in the interplay between short range forces and the long range forces. At each time step you FFT to the magnetisation tensor and then multiply with the interaction tensor, then iFFT.
