An implicit approximate inverse preconditioner for saddle point problems

Electronic Transactions on Numerical Analysis

Volumn 37, Issue , 2010, Pages 173-188

  Borne, Sabine Le ^a   Ngufor, Che ^b  

^a TENNESSEE TECHNOLOGICAL UNIVERSITY   (United States)

^b GEORGE MASON UNIVERSITY   (United States)

Author keywords

Preconditioning; Saddle point problem

Indexed keywords

NUMERICAL ANALYSIS;

APPROXIMATE INVERSE PRECONDITIONER; BLOCK PRECONDITIONERS; CONSTRAINT EQUATION; IMPLICIT REPRESENTATION; ITERATIVE SOLUTIONS; PRECONDITIONING; SADDLE POINT MATRICES; SADDLE POINT PROBLEMS;

INVERSE PROBLEMS;

EID: 78651509425     PISSN: None     EISSN: 10689613     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

1. M. BENZI, G. H. GOLUB, AND J. LIESEN, Numerical solution of saddle point problems, Acta Numer., 14 (2005), pp. 1-137.
2. S. B̈ORM AND L. GRASEDYCK, HLIB version 1.3. Available at www.hlib.org.
3. S. B̈ORM, L. GRASEDYCK, AND W. HACKBUSCH, Hierarchical matrices, Lecture Notes No. 21, Max-Planck-Institute for Mathematics in the Sciences, Leipzig, Germany, 2003. Available online at www.mis.mpg.de/preprints/ln/, revised version June 2006.
4. A. C. DE NIET AND F. W. WUBS, Two preconditioners for saddle point problems in fluid flows, Internat. J. Numer. Methods Fluids, 54 (2007), pp. 355-377.
5. H. C. ELMAN, Preconditioning of the steady-state Navier-Stokes equations with low viscosity, SIAM J. Sci. Comp., 20 (1999), pp. 1299-1316.
6. H. C. ELMAN, V. E. HOWLE, J. SHADID, R. SHUTTLERWORTH, AND R. TUMARINO, Block preconditioners based on approximate commutators, SIAM J. Sci. Comput., 27 (2005), pp. 1651-1668.
7. H. C. ELMAN, D. LOGHIN, AND A. J. WATHEN, Preconditioning techniques for Newton's method for the incompressible Navier-Stokes equations, BIT, 43 (2003), pp. 961-974.
8. H. G. GOLUB AND A. J. WATHEN, An iteration for indefinite systems and its application to the Navier-Stokes equations, SIAM J. Sci. Comput., 19 (1998), pp. 530-539.
9. N. I. M. GOULD, M. E. HRIBAR, AND J. NOCEDAL, On the solution of equality constrained quadratic programming problems arising in optimization, SIAM J. Sci. Comput., 23 (2001), pp. 1376-1395.
10. L. GRASEDYCK AND W. HACKBUSCH, Construction and arithmetics of H-matrices, Computing, 70 (2003), pp. 295-334.
11. J. C. HAWS AND C. D MEYER, Preconditioning KKT systems, Technical Report M&CT-Tech-01-021, The Boing Company, 2003.
12. D. KAY, D. LOGHIN, AND A. WATHEN, A preconditioner for the steady-state Navier-Stokes equations, SIAM J. Sci. Comput., 24 (2002), pp. 237-256.
13. C. KELLER, N. I. M. GOULD, AND A. J. WATHEN, Constraint preconditioning for indefinite linear systems, SIAM J. Matrix Anal. Appl., 21 (2000), pp. 1300-1317.
14. S. LE BORNE, Hierarchical matrix preconditioners for the Oseen equations, Comput. Vis. Sci., 11 (2008), pp. 147-158.
15. S. LE BORNE, Preconditioned nullspace method for the two-dimensional Oseen problem, SIAM J. Sci. Comput., 31 (2009), pp. 2492-2509.
16. S. LE BORNE, L. GRASEDYCK, AND R. KRIEMANN, Domain-decomposition based H-LU preconditioners, in Domain Decomposition Methods in Science and Engineering XVI, O. B. Widlund and D. E. Keyes, eds., Lect. Notes Comput. Sci. Eng., Vol. 55, Springer, New York, 2006, pp. 661-668.
17. S. G. NASH AND A. SOFER, Preconditioning reduced matrices, SIAM J. Matrix Anal. Appl., 17 (1996), pp. 47-68.
18. M. A. OLSHANSKII AND Y. V. VASSILEVSKI, Pressure Schur complement preconditioners for the discrete Oseen problem, SIAM J. Sci. Comput., 29 (2007), pp. 2686-2704.
19. H. G. ROOS, M. STYNES, AND L. TOBISKA,Numerical methods for singularly perturbed differential equations: convection diffusion and flow problems, Computational Mathematics, Vol. 24, Springer, Berlin, 1996.
20. O. SCHENK AND K. GÄRTNER, Solving unsymmetric sparse systems of linear equations with PARDISO, Journal of Future Generation Computer Systems, 20 (2004), pp. 475-487.
21. O. SCHENK AND K. GÄRTNER, On fast factorization pivoting methods for sparse symmetric indefinite systems, Electron. Trans. Numer. Anal., 23 (2006), pp. 158-179. http://etna.math.kent.edu/vol.23.2006/pp158-179.dir.