Force-related nuts and bolts in the discretization toolkit for electromagnetics

How to deal with motion and forces, at the discrete level, is still an open problem, if we want the coupled discrete dynamical system that results from discretization to behave consistently (energy and momentum conservation, etc.). If discretization is conceived as putting together appropriate pieces of a toolkit, this raises the question of which pieces should correspond to items like Lorentz force, Laplace force, Poynting flux, etc. A few such objects (templates for software parts, to some extent) are described, and an approach to the discrete analogue of the Maxwell tensor is outlined. Index Terms--Discrete exterior calculus, forces, Laplace force, Lorentz force, Maxwell tensor.