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Shifted FSAI preconditioners for the efficient parallel solution of non‐linear groundwater flow models
Author(s) -
Ferronato M.,
Janna C.,
Pini G.
Publication year - 2011
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.3309
Subject(s) - preconditioner , discretization , coefficient matrix , linear system , mathematics , iterative method , inverse , computer science , flow (mathematics) , mathematical optimization , matrix (chemical analysis) , groundwater flow , algorithm , aquifer , groundwater , mathematical analysis , geometry , geology , geotechnical engineering , eigenvalues and eigenvectors , physics , materials science , quantum mechanics , composite material
SUMMARY The present paper investigates the performance of a shifted factorized sparse approximate inverse as a parallel preconditioner for the iterative solution to the linear systems arising in the finite element discretization of non‐linear groundwater flow models. The shift strategy is based on an inexpensive preconditioner update exploiting the structure of the coefficient matrix. The proposed algorithm is experimented with in the parallel simulation of a large‐scale real multi‐aquifer system characterized by a stochastic distribution of the hydraulic conductivity. The numerical results show that the shifted factorized sparse approximate inverse algorithm may yield an overall computational gain up to 300% with respect to the non‐shifted scheme with an excellent parallel efficiency. Copyright © 2011 John Wiley & Sons, Ltd.