A note on the solve phase of a multicore solver
JD Hogg, J. A. Scott · Science and Technology Facilities Council · 2010
When using a direct solver to solve large sparse linear systems of equations, the solve phase that follows the numerical factorization performs a relatively small proportion of the total number of numerical operations. However, it is responsible for a much higher proportion of the memory traffic. This makes it a potential bottleneck on newer multicore architectures that have a higher ratio of computational power to memory bandwidth than exhibited by traditional shared-memory parallel machines. In this note, we illustrate the problem through experiments and test a number of different approaches that aim to improve the performance of the solve phase on multicore machines. We extend the DAGbased approach that has been successfully used for the factorize phase on multicore machines to the solve phase and explore techniques for reducing memory throughput. Numerical experiments that illustrate the difficulties and the effectiveness of our approaches are performed on large-scale problems from practical applications using the sparse multicore solver HSL MA87.