A factored sparse approximate inverse preconditioned conjugate gradient solver on graphics processing units

Graphics Processing Units (GPUs) exhibit significantly higher peak performance than conventional CPUs. However, in general only highly parallel algorithms can exploit their potential. In this scenario, the iterative solution to sparse linear systems of equations could be carried out quite efficiently on a GPU as it requires only matrix-by-vector products, dot products, and vector updates. However, to be really effective, any iterative solver needs to be properly preconditioned and this represents a major bottleneck for a successful GPU implementation. Due to its inherent parallelism, the factored sparse approximate inverse (FSAI) preconditioner represents an optimal candidate for the conjugate gradient-like solution of sparse linear systems. However, its GPU implementation requires a nontrivial recasting of multiple computational steps. We present our GPU version of the FSAI preconditioner along with a set of results that show how a noticeable speedup with respect to a highly tuned CPU counterpart is obtained.