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.