Parallel multilevel block ILU preconditioning techniques for large sparse linear systems

Chi Shen; Jun Zhang; Kai Wang

doi:10.1109/IPDPS.2003.1213182

Parallel multilevel block ILU preconditioning techniques for large sparse linear systems

Chi Shen, Jun Zhang, Kai Wang

Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We present a class of parallel preconditioning strategies built on a multilevel block incomplete LU (ILU)factorization technique to solve large sparse linear systems on distributed memory parallel computers. The preconditioners are constructed by using the concept of block independent sets. Two algorithms for constructing block independent sets of a distributed sparse matrix are proposed. We compare a few implementations of the parallel multilevel ILU preconditioners with different block independent set algorithms and different coarse level solution strategies. We also use some diagonal thresholding and perturbation strategies to enhance factorization stability. Numerical experiments indicate that our parallel multilevel block ILU preconditioners are robust and efficient.

Original language	English
Title of host publication	Proceedings - International Parallel and Distributed Processing Symposium, IPDPS 2003
ISBN (Electronic)	0769519261, 9780769519265
DOIs	https://doi.org/10.1109/IPDPS.2003.1213182
State	Published - 2003
Event	International Parallel and Distributed Processing Symposium, IPDPS 2003 - Nice, France Duration: Apr 22 2003 → Apr 26 2003

Publication series

Name	Proceedings - International Parallel and Distributed Processing Symposium, IPDPS 2003

Conference

Conference	International Parallel and Distributed Processing Symposium, IPDPS 2003
Country/Territory	France
City	Nice
Period	4/22/03 → 4/26/03

Bibliographical note

Publisher Copyright:
© 2003 IEEE.

ASJC Scopus subject areas

Computational Theory and Mathematics
Theoretical Computer Science
Software

Access to Document

10.1109/IPDPS.2003.1213182

Cite this

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title = "Parallel multilevel block ILU preconditioning techniques for large sparse linear systems",

abstract = "We present a class of parallel preconditioning strategies built on a multilevel block incomplete LU (ILU)factorization technique to solve large sparse linear systems on distributed memory parallel computers. The preconditioners are constructed by using the concept of block independent sets. Two algorithms for constructing block independent sets of a distributed sparse matrix are proposed. We compare a few implementations of the parallel multilevel ILU preconditioners with different block independent set algorithms and different coarse level solution strategies. We also use some diagonal thresholding and perturbation strategies to enhance factorization stability. Numerical experiments indicate that our parallel multilevel block ILU preconditioners are robust and efficient.",

author = "Chi Shen and Jun Zhang and Kai Wang",

note = "Publisher Copyright: {\textcopyright} 2003 IEEE.; International Parallel and Distributed Processing Symposium, IPDPS 2003 ; Conference date: 22-04-2003 Through 26-04-2003",

year = "2003",

doi = "10.1109/IPDPS.2003.1213182",

language = "English",

series = "Proceedings - International Parallel and Distributed Processing Symposium, IPDPS 2003",

booktitle = "Proceedings - International Parallel and Distributed Processing Symposium, IPDPS 2003",

}

Shen, C, Zhang, J & Wang, K 2003, Parallel multilevel block ILU preconditioning techniques for large sparse linear systems. in Proceedings - International Parallel and Distributed Processing Symposium, IPDPS 2003., 1213182, Proceedings - International Parallel and Distributed Processing Symposium, IPDPS 2003, International Parallel and Distributed Processing Symposium, IPDPS 2003, Nice, France, 4/22/03. https://doi.org/10.1109/IPDPS.2003.1213182

Parallel multilevel block ILU preconditioning techniques for large sparse linear systems. / Shen, Chi; Zhang, Jun; Wang, Kai.
Proceedings - International Parallel and Distributed Processing Symposium, IPDPS 2003. 2003. 1213182 (Proceedings - International Parallel and Distributed Processing Symposium, IPDPS 2003).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - We present a class of parallel preconditioning strategies built on a multilevel block incomplete LU (ILU)factorization technique to solve large sparse linear systems on distributed memory parallel computers. The preconditioners are constructed by using the concept of block independent sets. Two algorithms for constructing block independent sets of a distributed sparse matrix are proposed. We compare a few implementations of the parallel multilevel ILU preconditioners with different block independent set algorithms and different coarse level solution strategies. We also use some diagonal thresholding and perturbation strategies to enhance factorization stability. Numerical experiments indicate that our parallel multilevel block ILU preconditioners are robust and efficient.

AB - We present a class of parallel preconditioning strategies built on a multilevel block incomplete LU (ILU)factorization technique to solve large sparse linear systems on distributed memory parallel computers. The preconditioners are constructed by using the concept of block independent sets. Two algorithms for constructing block independent sets of a distributed sparse matrix are proposed. We compare a few implementations of the parallel multilevel ILU preconditioners with different block independent set algorithms and different coarse level solution strategies. We also use some diagonal thresholding and perturbation strategies to enhance factorization stability. Numerical experiments indicate that our parallel multilevel block ILU preconditioners are robust and efficient.

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T3 - Proceedings - International Parallel and Distributed Processing Symposium, IPDPS 2003

BT - Proceedings - International Parallel and Distributed Processing Symposium, IPDPS 2003

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Parallel multilevel block ILU preconditioning techniques for large sparse linear systems

Abstract

Publication series

Conference

Bibliographical note

ASJC Scopus subject areas

Access to Document

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