Parallel 3-D spherical-harmonics transport methods

This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The authors have developed massively parallel algorithms and codes for solving the radiation transport equation on 3-D unstructured spatial meshes consisting of arbitrary combinations of hexahedra, wedges, pyramids, and tetrahedra. Three self-adjoint forms of the transport equation are solved: the even-parity form, the odd-parity form, and the self-adjoint angular flux form. The authors developed this latter form, which offers several significant advantages relative to the traditional forms. The transport equation is discretized in space using a trilinear finite-element approximation, in direction using a spherical-harmonic approximation, and in energy using the multigroup approximation. The discrete equations are solved used a parallel conjugate-gradient. All of the parallel algorithms were implemented on the CM-5 computer at LANL. Calculations are presented which demonstrate that the solution technique is both highly parallel and efficient