Incomplete Sparse Approximate Inverses for Parallel Preconditioning

Anzt, Hartwig; Huckle, Thomas K.; Bräckle, Jürgen; Dongarra, Jack

doi:10.1016/j.parco.2017.10.003

Incomplete Sparse Approximate Inverses for Parallel Preconditioning

Journal Article · Sat Oct 28 00:00:00 EDT 2017 · Parallel Computing

DOI:https://doi.org/10.1016/j.parco.2017.10.003· OSTI ID:1407456

Anzt, Hartwig ^[1]; Huckle, Thomas K. ^[2]; Bräckle, Jürgen ^[2]; Dongarra, Jack ^[3]

Karlsruhe Inst. of Technology (KIT) (Germany); Univ. of Tennessee, Knoxville, TN (United States). Innovative Computing Lab.; University of Tennessee
Technical Univ. of Munich (Germany). Dept. of Informatics
Univ. of Tennessee, Knoxville, TN (United States). Innovative Computing Lab.; Univ. of Manchester (United Kingdom). School of Computer Science; Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

In this study, we propose a new preconditioning method that can be seen as a generalization of block-Jacobi methods, or as a simplification of the sparse approximate inverse (SAI) preconditioners. The “Incomplete Sparse Approximate Inverses” (ISAI) is in particular efficient in the solution of sparse triangular linear systems of equations. Those arise, for example, in the context of incomplete factorization preconditioning. ISAI preconditioners can be generated via an algorithm providing fine-grained parallelism, which makes them attractive for hardware with a high concurrency level. Finally, in a study covering a large number of matrices, we identify the ISAI preconditioner as an attractive alternative to exact triangular solves in the context of incomplete factorization preconditioning.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Tennessee, Knoxville, TN (United States)

Sponsoring Organization:: USDOE; USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

Grant/Contract Number:: SC0016513

OSTI ID:: 1407456

Alternate ID(s):: OSTI ID: 1511776

Journal Information:: Parallel Computing, Journal Name: Parallel Computing Vol. 71; ISSN 0167-8191

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
approximate sparse triangular solves
incomplete LU factorization
incomplete sparse approximate inverse
parallel computing
preconditioning

Incomplete Sparse Approximate Inverses for Parallel Preconditioning

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References (26)

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