As was done in Ref. [5], we have extended the SIMC algorithm by associating a vector of weights, indexed by the frequency group, for each photon simulated. Instead of sampling the line profile for spontaneously emitted photons as is the case for IMC, this method constructs the vector of weights by assigning to each emission frequency the birth weight times the emission probability for that frequency. Unlike Ref. [5], we do not collapse the weight vector to a single frequency at the end of time step. Instead, we carry the vector of weights through successive time steps, obtaining deterministic spectral information when the particle leaves the problem domain.
The weight vector approach, in the absence of frequency dependent physical scattering (e.g. Compton Scattering), handles frequency space deterministically. The role of Monte Carlo is then relegated to integrating the possibly complicated geometry of the problem. This approach has a significant advantage over frequency sampling when the frequencies with a high emission probability are also strongly absorbed, with photons being transported elsewhere in the frequency spectrum. An example, demonstrated in this paper, is the case of line transport with a high opacity at line center where most of the transport occurs in the wings of the line. Using the weight vector approach, every photon samples the important frequency region where transport occurs and develops the correct output spectrum for the geometrical path being sampled.