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Journal of Applied Mathematics
Volume 2012, Article ID 872901, 14 pages
Research Article

Parallel Rayleigh Quotient Optimization with FSAI-Based Preconditioning

Department of Mathematical Methods and Models for Scientific Applications, University of Padova, Via Trieste 63, 35121 Padova, Italy

Received 2 November 2011; Revised 1 February 2012; Accepted 3 February 2012

Academic Editor: Massimiliano Ferronato

Copyright © 2012 Luca Bergamaschi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The present paper describes a parallel preconditioned algorithm for the solution of partial eigenvalue problems for large sparse symmetric matrices, on parallel computers. Namely, we consider the Deflation-Accelerated Conjugate Gradient (DACG) algorithm accelerated by factorized-sparse-approximate-inverse- (FSAI-) type preconditioners. We present an enhanced parallel implementation of the FSAI preconditioner and make use of the recently developed Block FSAI-IC preconditioner, which combines the FSAI and the Block Jacobi-IC preconditioners. Results onto matrices of large size arising from finite element discretization of geomechanical models reveal that DACG accelerated by these type of preconditioners is competitive with respect to the available public parallel hypre package, especially in the computation of a few of the leftmost eigenpairs. The parallel DACG code accelerated by FSAI is written in MPI-Fortran 90 language and exhibits good scalability up to one thousand processors.