2015/09/25 by Ang Li, Radu Serban, Li, Ang +3 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Distributed #Electromagnetic Scattering and Analysis #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Software (cs.MS) #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations #Parallel #and Cluster Computing (cs.DC)
paper · pdf · doi:10.48550/arxiv.1509.07919
openalex publication_date 2015/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We discuss an approach for solving sparse or dense banded linear systems \bf A \bf x = \bf b on a Graphics Processing Unit (GPU) card. The matrix \bf A ∈ ℝN × N is possibly nonsymmetric and moderately large; i.e., 10000 ≤ N ≤ 500000. The \it split and parallelize (\tt SaP) approach seeks to partition the matrix \bf A into diagonal sub-blocks \bf Ai, i=1,…,P, which are independently factored in parallel. The solution may choose to consider or to ignore the matrices that couple the diagonal sub-blocks \bf Ai. This approach, along with the Krylov subspace-based iterative method that it preconditions, are implemented in a solver called \tt SaP::GPU, which is compared in terms of efficiency with three commonly used sparse direct solvers: \tt PARDISO, \tt SuperLU, and \tt MUMPS. \tt SaP::GPU, which runs entirely on the GPU except several stages involved in preliminary row-column permutations, is robust and compares well in terms of efficiency with the aforementioned direct solvers. In a comparison against Intel's \tt MKL, \tt SaP::GPU also fares well when used to solve dense banded systems that are close to being diagonally dominant. \tt SaP::GPU is publicly available and distributed as open source under a permissive BSD3 license.