Massively parallel red-black algorithms for x-y-z response matrix equations
Ulf R. Hanebutte, K.F. Laurin-Kovitz, Elmer E. Lewis · Transactions of the American Nuclear Society · 1992
Recently, both discrete ordinates and spherical harmonic (S[sub n] and P[sub n]) methods have been cast in the form of response matrices. In x-y geometry, massively parallel algorithms have been developed to solve the resulting response matrix equations on the Connection Machine family of parallel computers, the CM-2, CM-200, and CM-5. These algorithms utilize two-cycle iteration on a red-black checkerboard. In this work we examine the use of massively parallel red-black algorithms to solve response matric equations in three dimensions. This longer term objective is to utilize massively parallel algorithms to solve S[sub n] and/or P[sub n] response matrix problems. In this exploratory examination, however, we consider the simple 6 [times] 6 response matrices that are derivable from fine-mesh diffusion approximations in three dimensions.