Solution of Single Tridiagonal Linear Systems and Vectorization of the ICCG Algorithm on the Cray-1

Abstract

This chapter presents the solution of single tridiagonal linear systems and vectorization of the ICCG algorithm on the Cray-1. When the numerical algorithms used to solve the physics equations in codes which model laser fusion are examined, it is found that a large number of subroutines require the solution of tridiagonal linear systems of equations. Radiation transport, thermal- and suprathermal-electron transport, ion thermal conduction, charged-particle, and neutron transport require the solution of tridiagonal systems of equations. The standard algorithm that has been used in the past on CDC 7600s will not vectorize and hence, cannot take advantage of the large speed increases possible on the Cray-1 through vectorization. There is an alternative algorithm for solving tridiagonal systems called cyclic reduction, which allows for vectorization, and is optimal for the Cray-1. Software based on this algorithm is being used in LASNEX to solve tridiagonal linear systems in the subroutines. The new algorithm runs five times faster than the standard algorithm on the Cray-1.