Updating Incomplete Factorization Preconditioners for Model Order Reduction

TitleUpdating Incomplete Factorization Preconditioners for Model Order Reduction
Publication TypeJournal Article
Year of Publication2016
AuthorsAnzt, H., E. Chow, J. Saak, and J. Dongarra
JournalNumerical Algorithms
Volume73
Issue3
Number3
Pagination611–630
Date Published02-2016
Keywordskey publication
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.

DOI10.1007/s11075-016-0110-2