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The continuity equation for electromagnetic (EM) energy flow is used to describe radiation flow in the transport regime. The scheme of a discrete representation of Hz and a stochastic representation of Hx, Hy gives an effectively continuous representation of directed energy in the x-y plane, such that the ray effect of transport theory is absent. Since the in-plane amplitudes are generated at each time step, it is necessary to store only the perpendicular amplitudes and the results appear to be robust with respect to the coarse of this discretization

Use of the continuity equation for electromagnetic energy flow to describe radiation transport