On finding approximate supernodes for an efficient block-ILU(k) factorization

Parallel Computing

Volumn 34, Issue 6-8, 2008, Pages 345-362

  Hénon, Pascal ^a   Ramet, Pierre ^a   Roman, Jean ^a  

^a UNIVERSITÉ BORDEAUX 1   (France)

Author keywords

High performance computing; Incomplete ILU factorization; Sparse linear algebra

Indexed keywords

APPROXIMATION ALGORITHMS; ITERATIVE METHODS; LINEAR ALGEBRA; PROBLEM SOLVING;

HIGH PERFORMANCE COMPUTING; INCOMPLETE ILU FACTORIZATION; SPARSE LINEAR ALGEBRA;

FACTORIZATION;

EID: 44349149850     PISSN: 01678191     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.parco.2007.12.003     Document Type: Article

References (28)

1. Amestoy P.R., Guermouche A., L'Excellent J.-Y., and Pralet S. Hybrid scheduling for the parallel solution of linear systems. Parallel Computing 32 2 (2006) 136-156
2. Karypis G., and Kumar V. A fast and high-quality multi-level scheme for partitioning irregular graphs. SIAM Journal on Scientific Computing 20 (1998) 359-392
3. Duff I.S., Erisman A.M., and Reid J.K. Direct Methods for Sparse Matrices (1986), Clarendon Press, Oxford
4. George J.A., and Liu J.W.-H. Computer Solution of Large Sparse Positive Definite Systems (1981), Prentice-Hall, Englewood Cliffs, NJ
5. Amestoy P.R., Davis T.A., and Duff I.S. An approximate minimum degree ordering algorithm. SIAM Journal on Matrix Analysis and Applications 17 (1996) 886-905
6. Amestoy P.R., Duff I.S., Pralet S., and Vömel C. Adapting a parallel sparse direct solver to architectures with clusters of SMPs. Parallel Computing 29 11-12 (2003) 1645-1668
7. Saad Y. Iterative Methods for Sparse Linear Systems. second ed. (2003), SIAM, Philadelphia, PA
8. Chapman A., and Saad Y. Deflated and augmented Krylov subspace techniques. Numerical Linear Algebra with Applications 4 (1997) 43-66
9. Y. Campbell, T.A. Davis, Incomplete LU factorization: a multifrontal approach. .
10. Chang T.F., and Vassilevski P.S. A framework for block ILU factorizations using block-size reduction. Mathematics of Computation 64 (1995)
11. Charrier P., and Roman J. Algorithmique et calculs de complexité pour un solveur de type dissections emboî tées. Numerische Mathematik 55 (1989) 463-476
12. Gupta A. Recent progress in general sparse direct solvers. Lecture Notes in Computer Science 2073 (2001) 823-840
13. Hénon P., Ramet P., and Roman J. PaStiX: a high-performance parallel direct solver for sparse symmetric definite systems. Parallel Computing 28 2 (2002) 301-321
14. P. Hénon, P. Ramet, J. Roman, Efficient algorithms for direct resolution of large sparse system on clusters of SMP nodes, in: SIAM Conference on Applied Linear Algebra, Williamsburg, Virginie, USA, July 2003.
15. G. Karypis, V. Kumar, Parallel threshold-based ILU factorization, in: Proceedings of the IEEE/ACM SC97 Conference, 1997.
16. X.S. Li, J.W. Demmel, A scalable sparse direct solver using static pivoting, in: Proceedings of the Ninth SIAM Conference on Parallel Processing for Scientific Computing, San Antonio, Texas, March 22-24, 1999.
17. Liu J.W.H. The role of elimination trees in sparse factorization. SIAM Journal on Matrix Analysis and Applications 11 (1990) 134-172
18. Hysom D., and Pothen A. A scalable parallel algorithm for incomplete factor preconditioning. SIAM Journal on Scientific Computing 22 6 (2001) 2194-2215
19. Rose D.J., and Tarjan R.E. Algorithmic aspects of vertex elimination on directed graphs. SIAM Journal on Applied Mathematics 34 (1978) 176-197
20. Liu J.W.H., Ng E.G., and Peyton B.W. On finding supernodes for sparse matrix computations. SIAM Journal on Matrix Analysis and Applications 14 1 (1993) 242-252
21. Magolu monga Made M., and Van der Vorst A. A generalized domain decomposition paradigm for parallel incomplete LU factorization preconditionings. Future Generation Computer Systems 17 8 (2001) 925-932
22. F. Pellegrini, Scotch 4.0 User's guide, Technical Report, INRIA Futurs, April 2005. Available from: .
23. B. Hendrickson, R. Leland, An improved spectral graph partitioning algorithm for mapping parallel computations, Technical Report SAND92-1460, UC-405, Sandia National Laboratories, Albuquerque, NM, 1992.
24. Pellegrini F., Roman J., and Amestoy P. Hybridizing nested dissection and halo approximate minimum degree for efficient sparse matrix ordering. Concurrency: Practice and Experience 12 (2000) 69-84
25. Raghavan P., Teranishi K., and Ng E.G. A latency tolerant hybrid sparse solver using incomplete Cholesky factorization. Numerical Linear Algebra (2003)
26. Saad Y. ILUT: a dual threshold incomplete ILU factorization. Numerical Linear Algebra with Applications 1 (1994) 387-402
27. Saad Y. Iterative Methods for Sparse Linear Systems. second ed. (2003), SIAM
28. Watts Jr. J.W. A conjugate gradient truncated direct method for the iterative solution of the reservoir simulation pressure equation. Society of Petroleum Engineers Journal 21 (1981) 345-353