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Efficient parallel solution to large-size sparse eigenproblems with block FSAI preconditioning

Authors

  • Massimiliano Ferronato,

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    • Department of Mathematical Methods and Models for Scientific Applications, University of Padova, via Trieste 63, 35121 Padova, Italy
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  • Carlo Janna,

    1. Department of Mathematical Methods and Models for Scientific Applications, University of Padova, via Trieste 63, 35121 Padova, Italy
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  • Giorgio Pini

    1. Department of Mathematical Methods and Models for Scientific Applications, University of Padova, via Trieste 63, 35121 Padova, Italy
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Massimiliano Ferronato, Department of Mathematical Methods and Models for Scientific Applications, University of Padova, via Trieste 63, 35121 Padova, Italy.

E-mail: ferronat@dmsa.unipd.it

SUMMARY

The choice of the preconditioner is a key factor to accelerate the convergence of eigensolvers for large-size sparse eigenproblems. Although incomplete factorizations with partial fill-in prove generally effective in sequential computations, the efficient preconditioning of parallel eigensolvers is still an open issue. The present paper describes the use of block factorized sparse approximate inverse (BFSAI) preconditioning for the parallel solution of large-size symmetric positive definite eigenproblems with both a simultaneous Rayleigh quotient minimization and the Jacobi–Davidson algorithm. BFSAI coupled with a block diagonal incomplete decomposition proves a robust and efficient parallel preconditioner in a number of test cases arising from the finite element discretization of 3D fluid-dynamical and mechanical engineering applications, outperforming FSAI even by a factor of 8 and exhibiting a satisfactory scalability. Copyright © 2011 John Wiley & Sons, Ltd.

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