Incremental incomplete LU factorizations with applications

Numerical Linear Algebra with Applications

Volumn 17, Issue 5, 2010, Pages 811-837

  Calgaro, Caterina ^a,b   Chehab, Jean Paul ^b,c   Saad, Yousef ^d  

^a UNIV LILLE   (France)

^b INRIA   (France)

^c UNIVERSITÉ DE PICARDIE JULES VERNE   (France)

^d UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Incomplete LU factorization; Incremental LU; Preconditioning

Indexed keywords

EID: 78650344807     PISSN: 10705325     EISSN: 10991506     Source Type: Journal    
DOI: 10.1002/nla.756     Document Type: Article

References (31)

1. Saad Y. Iterative Methods for Sparse Linear Systems (2nd edn). SIAM: Philadelpha, PA, 2003.
2. Axelsson O. Iterative Solution Methods. Cambridge University Press: New York, 1994.
3. Birken P, Tebbens JD, Meister A, Tuma M. Preconditioner updates applied to CFD model problems. Applied Numerical Mathematics 2008; 58(11):1628-1641.
4. Chan SM, Brandwajn V. Partial matrix refactorization. IEEE Power Industry Computer Application Conference, San Francisco, CA, vol. PWRS-1(1). IEEE Power Engineering Society, 6-10 May 1986; 193-199.
5. Chehab J-P, Laminie J. Differential equations and solution of linear systems. Numerical Algorithms 2005; 40:103-124.
6. Chehab J-P. Matrix differential equations and inverse preconditioners. Computational and Applied Mathematics 2007; 26:95-128.
7. Benzi M, Meyer CD, TÅuma M. A sparse approximate inverse preconditioner for the conjugate gradient method. SIAM Journal on Scientific Computing 1996; 17:1135-1149.
8. Benzi M, Kouhia R, TÅuma M. Stabilized and block approximate inverse preconditioners for problems in solid and structural mechanics. Computational Methods in Applied Mechanics and Engineering 2001; 190:6533-6554.
9. Benzi M, TÅuma M. A sparse approximate inverse preconditioner for nonsymmetric linear systems. SIAM Journal on Scientific Computing 1998; 19:968-994.
10. Kolotinina LY, Yeremin AY. Incomplete block factorizationsas preconditioners for sparse spd matrices. Recent Advances in Iterative Methods, IMA Volumes in Mathematics and its Applications, vol. 60. Springer: New York, 1994.
11. Kolotilina LY, Yeremin AY. On a family of two-level preconditionings of the incomplete block factorization type. Soviet Journal of Numerical Analysis and Mathematical Modeling 1986; 1:293-320.
12. Kolotilina LY, Yeremin AY. Factorized sparse approximate inverse preconditionings I. Theory. SIAM Journal on Matrix Analysis and Applications 1993; 14:45-58.
13. Grote M, Simon HD. Parallel preconditioning and approximate inverses on the connection machine. In Parallel Processing for Scientific Computing, Sincovec RF, Keyes DE, Petzold LR, Reed DA (eds), vol. 2. SIAM: Philadelphia, PA, 1992; 519-523.
14. Grote MJ, Huckle T. Parallel preconditionings with sparse approximate inverses. SIAM Journal on Scientific Computing 1997; 18:838-853.
15. Chow E, Saad Y. Approximate inverse preconditioners via sparse-sparse iterations. SIAM Journal on Scientific Computing 1998; 19:995-1023.
16. Chow E, Saad Y. Approximate inverse techniques for block-partitioned matrices. SIAM Journal on Scientific Computing 1997; 18:1657-1675.
17. Holland RM, Wathen AJ, Shaw G. Sparse approximate inverses and target matrices. SIAM Journal on Scientific Computing 2005; 26:1000-1011.
18. Davis TA. Direct Methods for Sparse Linear Systems. SIAM: Philadelphia, PA, 2006.
19. Gilbert JR, Peierls T. Sparse partial pivoting in time proportional to arithmetic operations. SIAM Journal on Scientific Computing 1988; 9:862-874.
20. Tinney WF, Brandwajn V, Chan SM. Sparse vector methods. IEEE Transactions on Power Apparatus and Systems 1985; PAS-104(2):295-301.
21. Golub GH, Loan CFV. Matrix Computations (3rd edn). Johns Hopkins University Press: Baltimore, MD, 1996.
22. Calgaro C, Creusé E, Goudon T. An hybrid finite volume-finite element method for variable density incompressible flows. Journal of Computational Physics 2008; 227:4671-4696.
23. Strang G. On the construction and comparison of difference schemes. SIAM Journal on Numerical Analysis 1968; 5:506-517.
24. Eymard R, Gallouët T, Herbin R. Finite volume methods. Handbook of Numerical Analysis, vol. VII. North-Holland: Amsterdam, 2000; 713-1020.
25. LeVeque RJ. Finite volume methods for hyperbolic problems. Cambridge Texts in Applied Mathematics. Cambridge University Press: Cambridge, 2002.
26. Girault V, Raviart P-A. Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms, Springer Series in Computational Mathematics, vol. 5. Springer: Berlin, 1986.
27. Ern A, Guermond J-L. Éléments finis: théorie, applications, mise en œuvre. vol. 36 of Mathématiques & Applications (Berlin) [Mathematics & Applications]. Springer: Berlin, 2002.
28. Guermond J-L, Quartapelle L. A projection FEM for variable density incompressible flows. Journal of Computational Physics 2000; 165:167-188.
29. Calgaro C, Deuring P, Jennequin D. A preconditioner for generalized saddle-point problems: application to 3d stationary Navier-Stokes equations. Numerical Methods for Partial Differential Equations 2006; 22:1289-1313.
30. Silvester D, Elman H, Kay D, Wathen A. Efficient preconditioning of the linearized Navier-Stokes equations for incompressible flow. Journal of Computational and Applied Mathematics 2001; 128:261-279.
31. Cahouet J, Chabard J-P. Some fast 3D finite element solvers for the generalized Stokes problem. International Journal for Numerical Methods in Fluids 1988; 8:865-895.