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FDTD electrodynamics of 1-electron atom in a central potential on a discrete space-time lattice

We revisit the formulation within the FDTD method of the Abraham-Lorentz model of a 1-electron atom coupling to an external electromagnetic field via the dipole interaction between the field and the moving charge. This classical problem is reformulated for a purely discrete space in discrete-time by specifying the electromagnetic potentials and the electron charge density only at discrete spatial points or edges in a mesh decomposition of space. A systematic simplicial complex structure is used which preserves classical field theorems such as Gauss's Law, Stokes' and Green's Theorems in the discrete domain. The role of the radiation reaction field which permeates the electron charge is identified.