Simulation with models based on partial differential equations often requires the solution of (sequences of) large and sparse algebraic linear systems. In multidimensional domains, preconditioned Krylov iterative solvers are often appropriate for these duties. Therefore, the search for efficient preconditioners for Krylov subspace methods is a crucial theme. Recent developments, especially in computing hardware, have renewed the interest in approximate inverse preconditioners in factorized form, because their application during the solution process can be more efficient. We present here some experiences focused on the approximate inverse preconditioners proposed by Benzi and Tůma from 1996 and the sparsification and inversion proposed by van Duin in 1999. Computational costs, reorderings and implementation issues are considered both on conventional and innovative computing architectures like Graphics Programming Units (GPUs). The research that led to the present paper was partially supported by a grant of the group GNCS of INdAM

Bertaccini, D., Filippone, S. (2016). Sparse approximate inverse preconditioners on high performance GPU platforms. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 71(3), 693-711 [10.1016/j.camwa.2015.12.008].

Sparse approximate inverse preconditioners on high performance GPU platforms

Bertaccini, Daniele
;
Filippone, Salvatore
2016-01-01

Abstract

Simulation with models based on partial differential equations often requires the solution of (sequences of) large and sparse algebraic linear systems. In multidimensional domains, preconditioned Krylov iterative solvers are often appropriate for these duties. Therefore, the search for efficient preconditioners for Krylov subspace methods is a crucial theme. Recent developments, especially in computing hardware, have renewed the interest in approximate inverse preconditioners in factorized form, because their application during the solution process can be more efficient. We present here some experiences focused on the approximate inverse preconditioners proposed by Benzi and Tůma from 1996 and the sparsification and inversion proposed by van Duin in 1999. Computational costs, reorderings and implementation issues are considered both on conventional and innovative computing architectures like Graphics Programming Units (GPUs). The research that led to the present paper was partially supported by a grant of the group GNCS of INdAM
2016
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/08 - ANALISI NUMERICA
English
Approximate inverses; GPU; Preconditioners; Sparse matrices
Approximate inverses; GPU; Preconditioners; Sparse matrices; Modeling and Simulation; Computational Theory and Mathematics; Computational Mathematics
https://www.mat.uniroma2.it/bertaccini/papers/Bertaccini-Filippone-CAMWA2016.pdf
Bertaccini, D., Filippone, S. (2016). Sparse approximate inverse preconditioners on high performance GPU platforms. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 71(3), 693-711 [10.1016/j.camwa.2015.12.008].
Bertaccini, D; Filippone, S
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/203655
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