Vectorization of transport and diffusion computations on the CDC Cyber 205

This work focuses on development and testing of alternative numerical methods and computational algorithms specifically designed for the vectorization of transport and diffusion computations on a Control Data Corporation (CDC) Cyber 205 vector computer. The first part of the report summarizes and compares two solution methods for the discrete ordinates approximation to the transport equation. Factors of 4 to 7 reduction in run times for certain large transport problems were achieved on a Cyber 205 as compared with run times on a CDC-7600. The second part of the paper deals with the solution of tridiagonal systems of linear equations which is a central part for several efficient numerical methods for multidimensional diffusion computations and which is also essential for fluid flow and other physics and engineering problems. Among the methods tested, a combined odd-even cyclic reduction and modified Cholesky factorization algorithm for solving linear symmetric positive definite tridiagonal systems is found to be the most effective for these systems on a Cyber 205. For large tridiagonal systems, computation with this algorithm is an order of magnitude faster on a Cyber 205 than computation with the best algorithm for tridiagonal systems on a CDC-7600