Multilevel approaches for FSAI preconditioning

Summary Factorized sparse approximate inverse (FSAI) preconditioners are robust algorithms for symmetric positive matrices, which are particularly attractive in a parallel computational environment because of their inherent and almost perfect scalability. Their parallel degree is even redundant with...

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Vydáno v:Numerical linear algebra with applications Ročník 25; číslo 5
Hlavní autoři: Magri, Victor A. P., Franceschini, Andrea, Ferronato, Massimiliano, Janna, Carlo
Médium: Journal Article
Jazyk:angličtina
Vydáno: Oxford Wiley Subscription Services, Inc 01.10.2018
Témata:
algebraic multilevel preconditioner
Algorithms
Computing time
domain decomposition
Domain decomposition methods
FSAI preconditioner
Mathematical analysis
Matrix methods
Preconditioning
sparse approximate inverse
ISSN:1070-5325, 1099-1506
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Shrnutí:Summary Factorized sparse approximate inverse (FSAI) preconditioners are robust algorithms for symmetric positive matrices, which are particularly attractive in a parallel computational environment because of their inherent and almost perfect scalability. Their parallel degree is even redundant with respect to the actual capabilities of the current computational architectures. In this work, we present two new approaches for FSAI preconditioners with the aim of improving the algorithm effectiveness by adding some sequentiality to the native formulation. The first one, denoted as block tridiagonal FSAI, is based on a block tridiagonal factorization strategy, whereas the second one, domain decomposition FSAI, is built by reordering the matrix graph according to a multilevel k‐way partitioning method followed by a bandwidth minimization algorithm. We test these preconditioners by solving a set of symmetric positive definite problems arising from different engineering applications. The results are evaluated in terms of performance, scalability, and robustness, showing that both strategies lead to faster convergent schemes regarding the number of iterations and total computational time in comparison with the native FSAI with no significant loss in the algorithmic parallel degree.
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ISSN:1070-5325
1099-1506
DOI:10.1002/nla.2183