Abstract
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.
Keywords
- Sparsity Pattern
- Approximate Inverse
- Nonsymmetric Linear System
- Nonsymmetric Case
- Diagonal Preconditioner
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bear, J.: Hydraulics of Groundwater. McGraw-Hill, New York (1979)
Benzi, M., Cullum, J.K., Tůma, M.: Robust approximate inverse preconditioning for the conjugate gradient method. SIAM J. Sci. Comput. 22, 1318–1332 (2000)
Benzi, M., Tůma, M.: A sparse approximate inverse preconditioner for nonsymmetric linear systems. SIAM J. Sci. Comput. 19, 968–994 (1998)
Benzi, M., Tůma, M.: A comparative study of sparse approximate inverse preconditioners. Applied Numerical Mathematics 30, 305–340 (1999)
Benzi, M., Marin, J., Tůma, M.: A two-level parallel preconditioner based on sparse approximate inverses. In: Kincaid, D.R., Elster, A.C. (eds.) Iterative Methods in Scientific Computation IV, New Brunswick, New Jersey, USA. IMACS Series in Computational and Applied Mathematics, vol. 5, pp. 167–178 (1999)
Bergamaschi, L., Martínez, A., Pini, G.: Parallel solution of sparse eigenproblems by simultaneous Rayleigh quotient optimization with FSAI preconditioning. In: Joubert, G.R., Nagel, W. (eds.) Parallel Computing. Software Technology, Algorithms, Architectures & Applications, pp. 275–282. Elsevier, North-Holland (2004)
Bergamaschi, L., Putti, M.: Efficient parallelization of preconditioned conjugate gradient schemes for matrices arising from discretizations of diffusion equations. In: Proceedings of the Ninth SIAM Conference on Parallel Processing for Scientific Computing (March 1999); CD–Rom
Chow, E.: Parallel implementation and practical use of sparse approximate inverse preconditioners with a priori sparsity patterns. Intl. J. High Perf. Comput. Appl. 15, 56–74 (2001)
Grote, M.J., Huckle, T.: Parallel preconditioning with sparse approximate inverses. SIAM J. Sci. Comput. 18, 838–853 (1997)
Hysom, D., Pothen, A.: A scalable parallel algorithm for incomplete factor preconditioning. SIAM J. Sci. Comput. 22, 2194–2215 (2001)
Kaporin, I.E.: New convergence results and preconditioning strategies for the conjugate gradient method. Numer. Lin. Alg. Appl. 1, 179–210 (1994)
Kolotilina, L.Y., Nikishin, A.A., Yeremin, A.Y.: Factorized sparse approximate inverse preconditionings IV, Simple approaches to rising efficiency. Numer. Lin. Alg. Appl. 6, 515–531 (1999)
Kolotilina, L.Y., Yeremin, A.Y.: Factorized sparse approximate inverse preconditionings I. Theory. SIAM J. Matrix Anal. 14, 45–58 (1993)
Li, Z., Saad, Y., Sosonkina, M.: pARMS: a parallel version of the algebraic recursive multilevel solver. Numer. Linear Algebra Appl. 10, 485–509 (2003); Preconditioning, Tahoe City, CA (2001)
Nikishin, A.A., Yeremin, A.Y.: Prefiltration technique via aggregation for constructing low-density high-quality factorized sparse approximate inverse preconditionings. Numer. Linear Alg. Appl. 10, 235–246 (2003)
Saad, Y.: A flexible inner-outer preconditioned GMRES algorithm. SIAM J. Sci. Comput. 14, 461–469 (1993)
Saad, Y.: ILUT: A dual threshold incomplete ILU factorization. Num. Lin. Alg. Appl. 1, 387–402 (1994)
van der Vorst, H.A.: Bi-CGSTAB: A fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 13, 631–644 (1992)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bergamaschi, L., Martínez, Á. (2005). Parallel Acceleration of Krylov Solvers by Factorized Approximate Inverse Preconditioners. In: Daydé, M., Dongarra, J., Hernández, V., Palma, J.M.L.M. (eds) High Performance Computing for Computational Science - VECPAR 2004. VECPAR 2004. Lecture Notes in Computer Science, vol 3402. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11403937_47
Download citation
DOI: https://doi.org/10.1007/11403937_47
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25424-9
Online ISBN: 978-3-540-31854-5
eBook Packages: Computer ScienceComputer Science (R0)