Parallel Acceleration of Krylov Solvers by Factorized Approximate Inverse Preconditioners

This paper describes and tests a parallel implementation of a factorized approximate inverse preconditioner (FSAI) to accelerate iterative linear system solvers. Such a preconditioner reveals an efficient accelerator of both Conjugate gradient and BiCGstab iterative methods in the parallel solution of large linear systems arising from the discretization of the advection-diffusion equation. The resulting message passing code allows the solution of large problems leading to a very cost-effective algorithm for the solution of large and sparse linear systems.

[1]  Igor E. Kaporin,et al.  New convergence results and preconditioning strategies for the conjugate gradient method , 1994, Numer. Linear Algebra Appl..

[2]  Yousef Saad,et al.  ILUT: A dual threshold incomplete LU factorization , 1994, Numer. Linear Algebra Appl..

[3]  Masha Sosonkina,et al.  pARMS: a parallel version of the algebraic recursive multilevel solver , 2003, Numer. Linear Algebra Appl..

[4]  M. Benzi,et al.  A comparative study of sparse approximate inverse preconditioners , 1999 .

[5]  J. Bear.  Hydraulics of Groundwater , 1979 .

[6]  L. Kolotilina,et al.  Factorized Sparse Approximate Inverse Preconditionings I. Theory , 1993, SIAM J. Matrix Anal. Appl..

[7]  Alex Pothen,et al.  A Scalable Parallel Algorithm for Incomplete Factor Preconditioning , 2000, SIAM J. Sci. Comput..

[8]  Edmond Chow,et al.  Parallel Implementation and Practical Use of Sparse Approximate Inverse Preconditioners with a Priori Sparsity Patterns , 2001, Int. J. High Perform. Comput. Appl..

[9]  Luca Bergamaschi,et al.  Efficient Parallelization of Preconditioned Conjugate Gradient Scheme for Matrices Arising from Discretizations of Diffusion Equations , 1999, PPSC.

[10]  Henk A. van der Vorst,et al.  Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems , 1992, SIAM J. Sci. Comput..

[11]  Andy A. Nikishin,et al.  Prefiltration technique via aggregation for constructing low‐density high‐quality factorized sparse approximate inverse preconditionings , 2003, Numer. Linear Algebra Appl..

[12]  A. Yu. Yeremin,et al.  Factorized sparse approximate inverse preconditionings. IV: Simple approaches to rising efficiency , 1999 .

[13]  Luca Bergamaschi,et al.  Parallel Solution of Sparse Eigenproblems by Simultaneous Rayleigh Quotient Optimization with FSAI preconditioning , 2003, PARCO.

[14]  Yousef Saad,et al.  A Flexible Inner-Outer Preconditioned GMRES Algorithm , 1993, SIAM J. Sci. Comput..

[15]  YereminA. Yu.,et al.  Factorized sparse approximate inverse preconditionings I , 1993 .

[16]  Michele Benzi,et al.  Robust Approximate Inverse Preconditioning for the Conjugate Gradient Method , 2000, SIAM J. Sci. Comput..

[17]  Marcus J. Grote,et al.  Parallel Preconditioning with Sparse Approximate Inverses , 1997, SIAM J. Sci. Comput..

[18]  Michele Benzi,et al.  A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems , 1998, SIAM J. Sci. Comput..