A desirable choice for approximating the (1,1) block and the Schur complement relies on "naturally" parallel strategies, such as the factorized sparse approximate inverse (FSAI) [4], which however may prove generally much less effective than incomplete factorizations for several problems. A recent development in the field of parallel preconditioners for symmetric positive definite problems is the block FSAI incomplete Cholesky (BFSAI-IC) algorithm [5]. BFSAI-IC is a hybrid preconditioner coupling a novel approximate inverse based on the FSAI concept with a block diagonal incomplete factorization, proving generally superior to more traditional parallel preconditioners for any number of computing cores. The present work describes a novel parallel implementation of the inexact constraint preconditioner (ParICP) making use of BFSAI-IC as preconditioning kernel. The performance of ParICP with the symmetric quasi-minimal residual (SQMR) solver is experimented with in large size saddle-point problems arising from the finite element integration of the coupled consolidation equations. The results show that ParICP is a very efficient implementation of constraint preconditioning for high performance computing. In ill-conditioned saddle-point problems, ParICP appears to be a very promising and robust tool to obtain accurate solutions within a reasonable time.

1

L. Bergamaschi, J. Gondzio, G. Zilli, "Preconditioning indefinite systems in interior point methods for optimization", Computational Optimization with Applications, 28, 149-171, 2004. doi:10.1023/B:COAP.0000026882.34332.1b

2

L. Bergamaschi, M. Ferronato, G. Gambolati, "Mixed constraint preconditioners for the iterative solution to FE coupled consolidation equations", Journal of Computational Physics, 227, 9885-9897, 2008. doi:10.1016/j.jcp.2008.08.002

3

L. Bergamaschi, M. Ferronato, G. Gambolati, "Novel preconditioners for the iterative solution to FE-discretized coupled consolidation equations", Computer Methods in Applied Mechanics and Engineering, 196, 2647-2656, 2007. doi:10.1016/j.cma.2007.01.013

4

L.Yu. Kolotilina, A.Yu. Yeremin, "Factorized sparse approximate inverse preconditioning I. Theory", SIAM Journal on Matrix Analysis and Applications, 14, 45-58, 1993. doi:10.1137/0614004

5

C. Janna, M. Ferronato, G. Gambolati, "A block FSAI-ILU parallel preconditioner for symmetric positive definite linear systems", SIAM Journal on Scientific Computing, 32, 2468-2484, 2010. doi:10.1137/090779760

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