3-D deterministic transport methods research at LANL under ASCI - 285

The 3-D deterministic transport methods research that has been done at Los Alamos National Laboratory under the auspices of the ASCI program is briefly described, and future research directions are discussed. The research that has been done relates to the development of both numerical methods and parallel solution algorithms. Such methods and algorithms have been developed for the standard first-order form of the transport equation, second-order self-adjoint forms of the transport equation, S_N and P_n angular discretizations, and 3-D structured and unstructured meshes. New 3-D unstructured-mesh methods make it possible to efficiently apply the S_N method to problems with complex 3-D geometries. New parallel solution algorithms make it possible to perform calculations that are far beyond the capabilities of the best vector supercomputers. Nonetheless, there is much room for improvement in both numerical methods and parallel algorithms. The development of efficient parallel algorithms for the standard first-order S_N equations on unstructured meshes is a significant challenge, but the potential benefits of such methods are enormous. (author)