Mapping the preconditioned conjugate gradient algorithm for neutron diffusion applications onto parallel machines

This is a study of the performance on different parallel machines of the solution to the system of linear equations that results from the finite-differencing of the neutron diffusion equation in the context of nuclear reactor simulation. The solution approach uses the CG (conjugate gradient) and the PCG (preconditioned CG) methods. For PCG, a block preconditioner based on the incomplete Cholesky factorization was used. The issues involved in mapping the CG and the PCG algorithms onto the mixed-mode PASM prototype, the SIMD MasPar MP-1, and the MIMD Intel Paragon XPIS are discussed. On PASM, the mixed-mode implementation outperformed either SIMD or MIMD alone. Theoretical performance predictions were analyzed and compared with the experimental results on the MasPar MP-1 and the Paragon XPIS. Other issues addressed for all three machines include the impact on execution time of the number of processors used and the impact of the interprocessor communication network on performance.