Incomplete Sparse Approximate Inverses for Parallel Preconditioning

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 spars...

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Vydané v:Parallel computing Ročník 71
Hlavní autori: Anzt, Hartwig, Huckle, Thomas K., Bräckle, Jürgen, Dongarra, Jack
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: United States Elsevier 28.10.2017
Predmet:
approximate sparse triangular solves
incomplete LU factorization
incomplete sparse approximate inverse
MATHEMATICS AND COMPUTING
parallel computing
preconditioning
ISSN:0167-8191, 1872-7336
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Popis
Shrnutí: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.
Bibliografia:USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
SC0016513
USDOE National Nuclear Security Administration (NNSA)
ISSN:0167-8191
1872-7336