Discussion and Conclusions

We have presented our approach to the numerical solution to the generalized stellar atmosphere problem in the presence of rapidly expanding flows. We have shown how the use of accelerated $\Lambda$ operators may result in the formulation of the problem in such a way that extremely detailed model atoms may be handled in NLTE and the problem can be parallelized in a way that significantly reduces the per processor memory and CPU requirements with modest communication overhead. Parallelization also allows much more complex models to be calculations by giving us access to the large memory sizes that are available on modern parallel supercomputers. Currently, our largest model calculations involve 6000 atomic NLTE level with 65000 primary NLTE lines that are modeled individually, 2-10 million weak atomic secondary NLTE and LTE background lines and, for models of cool stellar winds, 150 million molecular lines. Simulations of this size and level of detail were simply not possible before the development of new radiative transfer algorithms and the availability of parallel supercomputers. We believe that the next step -- the computation of moving flows in three spatial dimensions, is becoming tractable on modern parallel supercomputers. There continues to be an urgent need for improvements in the fundamental atomic data which serves as input to these calculations.