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Article overview
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Analysis of A Splitting Approach for the Parallel Solution of Linear Systems on GPU Cards | | Ang Li
; Radu Serban
; Dan Negrut
; | | Date: |
26 Sep 2015 | | Abstract: | We discuss an approach for solving sparse or dense banded linear systems
${f A} {f x} = {f b}$ on a Graphics Processing Unit (GPU) card. The
matrix ${f A} in {mathbb{R}}^{N imes N}$ is possibly nonsymmetric and
moderately large; i.e., $10000 leq N leq 500000$. The ${it split and
parallelize}$ (${ t SaP}$) approach seeks to partition the matrix ${f A}$
into diagonal sub-blocks ${f A}_i$, $i=1,ldots,P$, which are independently
factored in parallel. The solution may choose to consider or to ignore the
matrices that couple the diagonal sub-blocks ${f A}_i$. This approach, along
with the Krylov subspace-based iterative method that it preconditions, are
implemented in a solver called ${ t SaP::GPU}$, which is compared in terms of
efficiency with three commonly used sparse direct solvers: ${ t PARDISO}$,
${ t SuperLU}$, and ${ t MUMPS}$. ${ t SaP::GPU}$, 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 ${ t MKL}$, ${ t SaP::GPU}$
also fares well when used to solve dense banded systems that are close to being
diagonally dominant. ${ t SaP::GPU}$ is publicly available and distributed as
open source under a permissive BSD3 license. | | Source: | arXiv, 1509.7919 | | Services: | Forum | Review | PDF | Favorites | |
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