Using Jacobi iterations and blocking for solving sparse triangular systems in incomplete factorization preconditioning

Chow, E., Hartwig, A., Scott, J. ORCID: https://orcid.org/0000-0003-2130-1091 and Dongarra, J. (2018) Using Jacobi iterations and blocking for solving sparse triangular systems in incomplete factorization preconditioning. Journal of Parallel and Distributed Computing, 119. pp. 219-230. ISSN 0743-7315 doi: 10.1016/j.jpdc.2018.04.017

Abstract/Summary

When using incomplete factorization preconditioners with an iterative method to solve large sparse linear systems, each application of the preconditioner involves solving two sparse triangular systems. These triangular systems are challenging to solve efficiently on computers with high levels of concurrency. On such computers, it has recently been proposed to use Jacobi iterations, which are highly parallel, to approximately solve the triangular systems from incomplete factorizations. The effectiveness of this approach, however, is problem-dependent: the Jacobi iterations may not always converge quickly enough for all problems. Thus, as a necessary and important step to evaluate this approach, we experimentally test the approach on a large number of realistic symmetric positive definite problems. We also show that by using block Jacobi iterations, we can extend the range of problems for which such an approach can be effective. For block Jacobi iterations, it is essential for the blocking to be cognizant of the matrix structure.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/77054
Item Type	Article
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Elsevier
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