A supernodal block factorized sparse approximate inverse for non-symmetric linear systems

The concept of supernodes, originally developed to accelerate direct solution methods for linear systems, is generalized to block factorized sparse approximate inverse (Block FSAI) preconditioning of non-symmetric linear systems. It is shown that aggregating the unknowns in clusters that are process...

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Vydáno v:Numerical algorithms Ročník 78; číslo 1; s. 333 - 354
Hlavní autoři: Ferronato, Massimiliano, Pini, Giorgio
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.05.2018
Springer Nature B.V
Témata:
Algebra
Algorithms
Computer Science
Iterative methods
Linear algebra
Linear systems
Numeric Computing
Numerical Analysis
Original Paper
Preconditioning
Theory of Computation
Linear systems
Parallel computing
65F10
68W10
Iterative methods
Preconditioning
65F08
65Y05
ISSN:1017-1398, 1572-9265
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Shrnutí:The concept of supernodes, originally developed to accelerate direct solution methods for linear systems, is generalized to block factorized sparse approximate inverse (Block FSAI) preconditioning of non-symmetric linear systems. It is shown that aggregating the unknowns in clusters that are processed together is particularly useful both to reduce the cost for the preconditioner setup and accelerate the convergence of the iterative solver. A set of numerical experiments performed on matrices arising from the meshfree discretization of 2D and 3D potential problems, where a very large number of nodal contacts is usually found, shows that the supernodal Block FSAI preconditioner outperforms the native algorithm and exhibits a much more stable behavior with respect to the variation of the user-specified parameters.
Bibliografie:ObjectType-Article-1
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-017-0378-x