Updating incomplete factorization preconditioners for model order reduction

Hartwig Anzt, Edmond Chow, Jens Saak, Jack Dongarra

    Research output: Contribution to journalArticlepeer-review

    Abstract

    When solving a sequence of related linear systems by iterative methods, it is common to reuse the preconditioner for several systems, and then to recompute the preconditioner when the matrix has changed significantly. Rather than recomputing the preconditioner from scratch, it is potentially more efficient to update the previous preconditioner. Unfortunately, it is not always known how to update a preconditioner, for example, when the preconditioner is an incomplete factorization. A recently proposed iterative algorithm for computing incomplete factorizations, however, is able to exploit an initial guess, unlike existing algorithms for incomplete factorizations. By treating a previous factorization as an initial guess to this algorithm, an incomplete factorization may thus be updated. We use a sequence of problems from model order reduction. Experimental results using an optimized GPU implementation show that updating a previous factorization can be inexpensive and effective, making solving sequences of linear systems a potential niche problem for the iterative incomplete factorization algorithm.

    Original languageEnglish
    Pages (from-to)611-630
    Number of pages20
    JournalNumerical Algorithms
    Volume73
    Issue number3
    Early online date23 Feb 2016
    DOIs
    Publication statusPublished - Nov 2016

    Keywords

    • Finegrained parallelism
    • GPU
    • Incomplete factorization
    • Model order reduction
    • Preconditioner update
    • Sequence of linear systems

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