SPIKE::GPU A SPIKE-based preconditioned GPU Solver for Sparse Linear Systems

This contribution outlines an approach that draws on general purpose graphics processing unit (GPGPU) computing to solve large linear systems. To methodology proposed relies on a SPIKE-based preconditioner with a Krylov-subspace method and has the following three stages: (i) row/column reordering for boosting diagonal dominance and reducing bandwidth; (ii) applying single precision truncated SPIKE on a dense banded matrix obtained after dropping small elements that fall outside a carefully selected bandwidth; and (iii) preconditioning within the BiCGStab(2) framework. The reordering strategy adopted aims at generating a narrow bandwidth dense matrix that is diagonally heavy. The results of several numerical experiments indicate that when used in conjunction with large dense banded matrices, the proposed approach is two to three times faster than the latest version of the MKL dense solver as soon as d > 0.23. When handling sparse systems, synthetic results obtained for large random matrices suggest that the proposed approach is three to five times faster than the PARDISO solver as long as the reordered matrices are close to being diagonally dominant. For a random set of smaller dimension application matrices, some out of the University of Florida Sparse Matrix Collection, the proposed approach is shown to be better or comparable in performance to PARDISO.