ParaSails is a parallel sparse approximate inverse preconditioner for the iterative solution of large, sparse systems of linear equations. It is a self-contained module in the HYPRE preconditioner library currently being developed at the Center for Applied Scientific Computing. ParaSails has been used to solve finite element elasticity problems inside an LLNL simulation code with more than 4 million equations on 1000 processors of ASCI Blue-Pacific (IBM SP). It has also been demonstrated on anisotropic diffusion problems with 216 million equations. ParaSails uses least-squares (Frobenius norm) minimization to compute a sparse approximate inverse. The sparsity pattern used is the pattern of a power of a sparsified matrix. ParaSails also uses a post-filtering technique to reduce the cost of applying the preconditioner. The pattern of the preconditioner can be reused to generate preconditioners for different matrices in a sequence of linear solves. ParaSails solves symmetric positive definite (SPD) problems using a factorized SPD preconditioner. ParaSails can also solve general (nonsymmetric and/or indefinite) problems with a nonfactorized preconditioner. The software available to be downloaded includes parallel CG and GMRES solvers, a parallel matrix class and a test driver.

References in zbMATH (referenced in 29 articles )

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  1. Carr, Arielle; de Sturler, Eric; Gugercin, Serkan: Preconditioning parametrized linear systems (2021)
  2. Milyukova, O. Yu.: MPI+OpenMP parallel implementation of conjugate gradient method with factored implicit preconditioners (2021)
  3. Bernaschi, Massimo; Carrozzo, Mauro; Franceschini, Andrea; Janna, Carlo: A dynamic pattern factored sparse approximate inverse preconditioner on graphics processing units (2019)
  4. Kyziropoulos, Panagiotis E.; Filelis-Papadopoulos, Christos K.; Gravvanis, George A.: A class of symmetric factored approximate inverses and hybrid two-level solver (2018)
  5. Moutafis, Byron E.; Filelis-Papadopoulos, Christos K.; Gravvanis, George A.: Parallel Schur complement techniques based on multiprojection methods (2018)
  6. Bu, Yiming; Carpentieri, Bruno; Shen, Zhaoli; Huang, Ting-Zhu: A hybrid recursive multilevel incomplete factorization preconditioner for solving general linear systems (2016)
  7. Sivas, Abdullah Ali; Manguoğlu, Murat; ten Thije Boonkkamp, J. H. M.; Anthonissen, M. J. H.: Discretization and parallel iterative schemes for advection-diffusion-reaction problems (2016)
  8. Bertolazzi, Enrico; Frego, Marco: Preconditioning complex symmetric linear systems (2015)
  9. Janna, Carlo; Ferronato, Massimiliano; Sartoretto, Flavio; Gambolati, Giuseppe: FSAIPACK: a software package for high-performance factored sparse approximate inverse preconditioning (2015)
  10. Kyziropoulos, P. E.; Filelis-Papadopoulos, C. K.; Gravvanis, G. A.: Parallel (N)-body simulation based on the PM and P3M methods using multigrid schemes in conjunction with generic approximate sparse inverses (2015)
  11. Alsing, Paul M.; Miller, Warner A.; Corne, Matthew; Gu, David; Lloyd, Seth; Ray, Shannon; Yau, Shing-Tung: Simplicial Ricci flow: an example of a neck pinch singularity in 3D (2014)
  12. Ballard, G.; Carson, E.; Demmel, J.; Hoemmen, M.; Knight, N.; Schwartz, O.: Communication lower bounds and optimal algorithms for numerical linear algebra (2014)
  13. Kaporin, I. E.: Using Chebyshev polynomials and approximate inverse triangular factorizations for preconditioning the conjugate gradient method (2012)
  14. Tang, Jok M.; Saad, Yousef: A probing method for computing the diagonal of a matrix inverse. (2012)
  15. Gupta, Anshul; George, Thomas: Adaptive techniques for improving the performance of incomplete factorization preconditioning (2010)
  16. Huckle, T.; Kallischko, A.; Roy, A.; Sedlacek, M.; Weinzierl, T.: An efficient parallel implementation of the MSPAI preconditioner (2010)
  17. Raghavan, Padma; Teranishi, Keita: Parallel hybrid preconditioning: incomplete factorization with selective sparse approximate inversion (2010)
  18. Malas, Tahir; Gürel, Levent: Accelerating the multilevel fast multipole algorithm with the sparse-approximate-inverse (SAI) preconditioning (2009)
  19. Uçar, Bora; Aykanat, Cevdet: Partitioning sparse matrices for parallel preconditioned iterative methods (2007)
  20. Chen, Ke; Hughes, Martyn D.: A two-level sparse approximate inverse preconditioner for unsymmetric matrices (2006)

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