A Splitting Approach for the Parallel Solution of Large Linear Systems on GPU Cards
Authors: Ang Li (University of Wisconsin-Madison), Radu Serban (University of Wisconsin-Madison), Dan Negrut (University of Wisconsin-Madison)
Abstract: We discuss a GPU solver for sparse or dense banded linear systems Ax=b, with A possibly nonsymmetric, sparse, and moderately large. The split and parallelize (SaP) approach seeks to partition the matrix A into P diagonal sub-blocks which are independently factored in parallel. The solution may choose to consider or to ignore the off-diagonal coupling blocks. This approach, along with the Krylov iterative methods that it preconditions, are implemented in the SaP::GPU solver, which runs entirely on the GPU except for several stages involved in preliminary row-column permutations.
SaP::GPU compares well in terms of efficiency with three commonly used sparse direct solvers: PARDISO, SuperLU, and MUMPS. Compared to Intel's MKL, SaP::GPU proves to also be performant on dense banded systems that are close to being diagonally dominant.
SaP::GPU is available open source under a permissive BSD3 license.
Two-page extended abstract: pdf