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 21 articles )

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  1. Bu, Yiming; Carpentieri, Bruno; Shen, Zhaoli; Huang, Ting-Zhu: A hybrid recursive multilevel incomplete factorization preconditioner for solving general linear systems (2016)
  2. Sivas, Abdullah Ali; Manguo\~glu, Murat; ten Thije Boonkkamp, J.H.M.; Anthonissen, M.J.H.: Discretization and parallel iterative schemes for advection-diffusion-reaction problems (2016)
  3. Janna, Carlo; Ferronato, Massimiliano; Sartoretto, Flavio; Gambolati, Giuseppe: FSAIPACK: a software package for high-performance factored sparse approximate inverse preconditioning (2015)
  4. 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)
  5. Kaporin, I.E.: Using Chebyshev polynomials and approximate inverse triangular factorizations for preconditioning the conjugate gradient method (2012)
  6. Tang, Jok M.; Saad, Yousef: A probing method for computing the diagonal of a matrix inverse. (2012)
  7. Gupta, Anshul; George, Thomas: Adaptive techniques for improving the performance of incomplete factorization preconditioning (2010)
  8. Huckle, T.; Kallischko, A.; Roy, A.; Sedlacek, M.; Weinzierl, T.: An efficient parallel implementation of the MSPAI preconditioner (2010)
  9. Raghavan, Padma; Teranishi, Keita: Parallel hybrid preconditioning: incomplete factorization with selective sparse approximate inversion (2010)
  10. Malas, Tahir; Gürel, Levent: Accelerating the multilevel fast multipole algorithm with the sparse-approximate-inverse (SAI) preconditioning (2009)
  11. Uçar, Bora; Aykanat, Cevdet: Partitioning sparse matrices for parallel preconditioned iterative methods (2007)
  12. Chen, Ke; Hughes, Martyn D.: A two-level sparse approximate inverse preconditioner for unsymmetric matrices (2006)
  13. Cullum, J.K.; Tůma, M.: Matrix-free preconditioning using partial matrix estimation (2006)
  14. Bergamaschi, Luca; Martínez, Ángeles: Parallel acceleration of Krylov solvers by factorized approximate inverse preconditioners (2005)
  15. Bencheva, G.; Margenov, S.: Parallel incomplete factorization preconditioning of rotated linear FEM systems (2003)
  16. Bergamaschi, Luca; Pini, Giorgio; Sartoretto, Flavio: Computational experience with sequential and parallel, preconditioned Jacobi--Davidson for large, sparse symmetric matrices (2003)
  17. Chow, Edmond; Manteuffel, Thomas A.; Tong, Charles; Wallin, Bradley K.: Algebraic elimination of slide surface constraints in implicit structural analysis (2003)
  18. Wang, Kai; Kim, Sangbae; Zhang, Jun: A comparative study on dynamic and static sparsity patterns in parallel sparse approximate inverse preconditioning (2003)
  19. Wang, Kai; Zhang, Jun: MSP: A class of parallel multistep successive sparse approximate inverse preconditioning strategies (2003)
  20. Yeremin, A.Yu.; Nikishin, A.A.: Factorized-sparse-approximate-inverse preconditionings of linear systems with unsymmetric matrices (2002)

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