MAPPING CONJUGATE-GRADIENT ALGORITHMS FOR NEUTRON DIFFUSION APPLICATIONS ONTO SIMD, MIMD, AND MIXED-MODE MACHINES

The performance of conjugate gradient (CG) algorithms for the solution of the system of linear equations that results from the finite-differ encing of the neutron diffusion equation was analyzed on SIMD, MIMD, a nd mixed-mode parallel machines. A block preconditioner based on the i ncomplete Cholesky factorization was used to accelerate the conjugate gradient search. The issues involved in mapping both the unpreconditio ned and preconditioned conjugate gradient algorithms onto the mixed-mo de PASM prototype; the SIMD MasPar MP-1, and the MIMD Intel Paragon XP /S are discussed. On PASM, the mixed-mode implementation outperformed either SIMD or MIMD alone. Theoretical performance predictions were an alyzed and compared with the experimental results on the MasPar MP-I a nd the Paragon XP/S. Other issues addressed include the impact on exec ution time of the number of processors used, the effect of the interpr ocessor communication network on performance, and the relationship of the number of processors to the quality of the preconditioning. Applic ations studies such as this are necessary in the development of softwa re tools for mapping algorithms onto either a single parallel machine or a heterogeneous suite of parallel machines.