Multigrid treatment and robustness enhancement for factored sparse approximate inverse preconditioning

Kai Wang; Jun Zhang

doi:10.1016/S0168-9274(02)00105-8

Multigrid treatment and robustness enhancement for factored sparse approximate inverse preconditioning

Kai Wang, Jun Zhang

Computer Science

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We investigate the use of sparse approximate inverse techniques (SAI) in a grid based multilevel ILU preconditioner (GILUM) to design a robust and parallelizable preconditioner for solving general sparse matrices. Taking the advantages of grid based multilevel methods, the resulting preconditioner outperforms sparse approximate inverse in robustness and efficiency. Conversely, taking the advantages of sparse approximate inverse, it affords an easy and convenient way to introduce parallelism within multilevel structure. Moreover, an independent set search strategy with automatic diagonal thresholding and a relative threshold dropping strategy are proposed to improve preconditioner performance. Numerical experiments are used to show the effectiveness and efficiency of the proposed preconditioner, and to compare it with some single and multilevel preconditioners.

Original language	English
Pages (from-to)	483-500
Number of pages	18
Journal	Applied Numerical Mathematics
Volume	43
Issue number	4
DOIs	https://doi.org/10.1016/S0168-9274(02)00105-8
State	Published - Dec 2002

Bibliographical note

Funding Information:
✩ This research was supported in part by the US National Science Foundation under grants CCR-9902022, CCR-9988165, and CCR-0092532. * Corresponding author. E-mail addresses: [email protected] (K. Wang), [email protected] (J. Zhang). URL address: http://www.cs.uky.edu/~jzhang.

Funding

✩ This research was supported in part by the US National Science Foundation under grants CCR-9902022, CCR-9988165, and CCR-0092532. * Corresponding author. E-mail addresses: [email protected] (K. Wang), [email protected] (J. Zhang). URL address: http://www.cs.uky.edu/~jzhang.

Funders	Funder number
National Science Foundation (NSF)	CCR-0092532, CCR-9902022, CCR-9988165

Keywords

Algebraic multigrid method
Incomplete LU factorization
Krylov subspace methods
Multilevel ILU preconditioner
Sparse approximate inverse
Sparse matrices

ASJC Scopus subject areas

Numerical Analysis
Computational Mathematics
Applied Mathematics

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10.1016/S0168-9274(02)00105-8

Cite this

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title = "Multigrid treatment and robustness enhancement for factored sparse approximate inverse preconditioning",

abstract = "We investigate the use of sparse approximate inverse techniques (SAI) in a grid based multilevel ILU preconditioner (GILUM) to design a robust and parallelizable preconditioner for solving general sparse matrices. Taking the advantages of grid based multilevel methods, the resulting preconditioner outperforms sparse approximate inverse in robustness and efficiency. Conversely, taking the advantages of sparse approximate inverse, it affords an easy and convenient way to introduce parallelism within multilevel structure. Moreover, an independent set search strategy with automatic diagonal thresholding and a relative threshold dropping strategy are proposed to improve preconditioner performance. Numerical experiments are used to show the effectiveness and efficiency of the proposed preconditioner, and to compare it with some single and multilevel preconditioners.",

keywords = "Algebraic multigrid method, Incomplete LU factorization, Krylov subspace methods, Multilevel ILU preconditioner, Sparse approximate inverse, Sparse matrices",

author = "Kai Wang and Jun Zhang",

note = "Funding Information: ✩ This research was supported in part by the US National Science Foundation under grants CCR-9902022, CCR-9988165, and CCR-0092532. * Corresponding author. E-mail addresses: [email protected] (K. Wang), [email protected] (J. Zhang). URL address: http://www.cs.uky.edu/~jzhang.",

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AU - Wang, Kai

AU - Zhang, Jun

N1 - Funding Information: ✩ This research was supported in part by the US National Science Foundation under grants CCR-9902022, CCR-9988165, and CCR-0092532. * Corresponding author. E-mail addresses: [email protected] (K. Wang), [email protected] (J. Zhang). URL address: http://www.cs.uky.edu/~jzhang.

PY - 2002/12

Y1 - 2002/12

N2 - We investigate the use of sparse approximate inverse techniques (SAI) in a grid based multilevel ILU preconditioner (GILUM) to design a robust and parallelizable preconditioner for solving general sparse matrices. Taking the advantages of grid based multilevel methods, the resulting preconditioner outperforms sparse approximate inverse in robustness and efficiency. Conversely, taking the advantages of sparse approximate inverse, it affords an easy and convenient way to introduce parallelism within multilevel structure. Moreover, an independent set search strategy with automatic diagonal thresholding and a relative threshold dropping strategy are proposed to improve preconditioner performance. Numerical experiments are used to show the effectiveness and efficiency of the proposed preconditioner, and to compare it with some single and multilevel preconditioners.

AB - We investigate the use of sparse approximate inverse techniques (SAI) in a grid based multilevel ILU preconditioner (GILUM) to design a robust and parallelizable preconditioner for solving general sparse matrices. Taking the advantages of grid based multilevel methods, the resulting preconditioner outperforms sparse approximate inverse in robustness and efficiency. Conversely, taking the advantages of sparse approximate inverse, it affords an easy and convenient way to introduce parallelism within multilevel structure. Moreover, an independent set search strategy with automatic diagonal thresholding and a relative threshold dropping strategy are proposed to improve preconditioner performance. Numerical experiments are used to show the effectiveness and efficiency of the proposed preconditioner, and to compare it with some single and multilevel preconditioners.

KW - Algebraic multigrid method

KW - Incomplete LU factorization

KW - Krylov subspace methods

KW - Multilevel ILU preconditioner

KW - Sparse approximate inverse

KW - Sparse matrices

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JF - Applied Numerical Mathematics

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ER -

Multigrid treatment and robustness enhancement for factored sparse approximate inverse preconditioning

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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