We have discussed the methods that we have implemented in PHOENIX to parallelize the calculation of wavelength dependent spectra (for both spectral synthesis and model atmosphere generation). While the algorithms are simple in the case of static stellar atmospheres, for moving atmospheres, e.g., the expanding atmospheres of novae and supernovae or stellar winds, the radiative transfer equation is coupled between different wavelengths. Therefore, we have developed a ``pipelined'' approach that is used in expanding atmosphere models to parallelize the spectrum calculation. Combined with the ``spatial'' and ``line'' data and task parallelization reported in paper I, this new parallelization option can dramatically increase the speed of very detailed and sophisticated NLTE and LTE stellar atmosphere calculation with PHOENIX. The parallelization has become a standard feature of the production version of PHOENIX and we are routinely using all 3 parallelization options simultaneously to calculate model atmospheres for a large variety of objects from Brown and M dwarfs to novae and supernovae on parallel supercomputers. This has drastically increased our productivity with a comparatively small time and coding investment. It also forms the basis to much larger calculations that will be required to appropriately analyze the much improved data that can be expected from future ground- and space-based observatories.
Our wavelength parallelization combines the methods described in paper I by combining a number of worker nodes (which employ the task and data parallel algorithms discussed in paper I) into symmetric ``wavelength clusters'' which work on different wavelength and that communicate results (if necessary) between them. This scheme is relatively simple to implement using the MPI standard and can be used on all parallel computers, both distributed and shared-memory systems (including clusters of workstations). It has the advantage of minimizing communication and it allows us to tailor the code's memory usage to the memory available on each individual node.
The behavior of the wavelength parallelization can be understood easily and the speedups are as expected. The parallel scalability of PHOENIX is comparable to or even better than that of many commercially available scientific applications. The potential of parallel computing for stellar atmosphere modeling is enormous, both in terms of problem size and speed to model construction. The aggregate memory and computing power of parallel supercomputers can be used to create extremely detailed models that are impossible to calculate on vector supercomputers or workstations.
Acknowledgments: We thank the referee, John Castor, for helpful comments that helped to greatly improve the manuscript. We also thank David Lowenthal for helpful discussions on parallel computing. This work was supported in part by NASA ATP grant NAG 5-3018 and LTSA grant NAG 5-3619 to the University of Georgia, and by NSF grant AST-9417242, NASA grant NAG5-3505 and an IBM SUR grant to the University of Oklahoma. Some of the calculations presented in this paper were performed on the IBM SP2 of the UGA UCNS, at the San Diego Supercomputer Center (SDSC), the Cornell Theory Center (CTC), and at the National Center for Supercomputing Applications (NCSA), with support from the National Science Foundation, and at the NERSC with support from the DoE. We thank all these institutions for a generous allocation of computer time.