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The Scientific World Journal
Volume 2013, Article ID 486323, 6 pages
http://dx.doi.org/10.1155/2013/486323
Research Article

Incomplete Augmented Lagrangian Preconditioner for Steady Incompressible Navier-Stokes Equations

1School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China
2Department of Information and Computational Science, Chengdu Technological University, Chengdu, Sichuan 611730, China

Received 16 July 2013; Accepted 29 August 2013

Academic Editors: I. Altun, S. Amat, and S. Hristova

Copyright © 2013 Ning-Bo Tan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. C. Elman, D. J. Silvester, and A. J. Wathen, Finite Elements and Fast Iterative Solvers: With Applications in Incompressible Fluid Dynamics, Numerical Mathematics and Scientific Computation, Oxford University Press, Oxford, UK, 2005.
  2. R. Glowinski, Handbook of Numerical Analysis: Numerical Methods for Fluids (Part 3), vol. 9, Elsevier, Amsterdam, The Netherlands, 2003.
  3. M. Benzi, G. H. Golubt, and J. Liesen, “Numerical solution of saddle point problems,” Acta Numerica, vol. 14, pp. 1–137, 2005. View at Publisher · View at Google Scholar · View at Scopus
  4. H. Elman, V. E. Howle, J. Shadid, D. Silvester, and R. Tuminaro, “Least squares preconditioners for stabilized discretizations of the Navier-Stokes equations,” SIAM Journal on Scientific Computing, vol. 30, no. 1, pp. 290–311, 2007. View at Publisher · View at Google Scholar · View at Scopus
  5. H. C. Elman and R. S. Tuminaro, “Boundary conditions in approximate commutator preconditioners for the navier-stokes equations,” Electronic Transactions on Numerical Analysis, vol. 35, pp. 257–280, 2009. View at Google Scholar · View at Scopus
  6. M. A. Olshanskii and Y. V. Vassilevski, “Pressure schur complement preconditioners for the discrete oseen problem,” SIAM Journal on Scientific Computing, vol. 29, no. 6, pp. 2686–2704, 2007. View at Publisher · View at Google Scholar · View at Scopus
  7. Z.-Z. Bai, G. H. Golub, and M. K. Ng, “Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems,” SIAM Journal on Matrix Analysis and Applications, vol. 24, no. 3, pp. 603–626, 2003. View at Publisher · View at Google Scholar · View at Scopus
  8. M. Benzi and G. H. Golub, “A preconditioner for generalized saddle point problems,” SIAM Journal on Matrix Analysis and Applications, vol. 26, no. 1, pp. 20–41, 2005. View at Publisher · View at Google Scholar · View at Scopus
  9. M. Benzi and J. Liu, “An efficient solver for the incompressible Navier-Stokes equations in rotation form,” SIAM Journal on Scientific Computing, vol. 29, no. 5, pp. 1959–1981, 2007. View at Publisher · View at Google Scholar · View at Scopus
  10. L. Chan, M. K. Ng, and N. Tsing, “Spectral analysis of the HSS preconditioners,” Numerical Mathematics, vol. 1, pp. 113–137, 2008. View at Google Scholar
  11. M. Benzi and X.-P. Guo, “A dimensional split preconditioner for Stokes and linearized Navier-Stokes equations,” Applied Numerical Mathematics, vol. 61, no. 1, pp. 66–76, 2011. View at Publisher · View at Google Scholar · View at Scopus
  12. M. Benzi, M. Ng, Q. Niu, and Z. Wang, “A relaxed dimensional factorization preconditioner for the incompressible Navier-Stokes equations,” Journal of Computational Physics, vol. 230, no. 16, pp. 6185–6202, 2011. View at Publisher · View at Google Scholar · View at Scopus
  13. M. Benzi and M. A. Olshanskii, “An augmented Lagrangian-based approach to the Oseen problem,” SIAM Journal on Scientific Computing, vol. 28, no. 6, pp. 2095–2113, 2006. View at Publisher · View at Google Scholar · View at Scopus
  14. M. A. Olshanskii and M. Benzi, “An augmented lagrangian approach to linearized problems in hydrodynamic stability,” SIAM Journal on Scientific Computing, vol. 30, no. 3, pp. 1459–1473, 2007. View at Publisher · View at Google Scholar · View at Scopus
  15. M. Benzi, M. A. Olshanskii, and Z. Wang, “Modified augmented Lagrangian preconditioners for the incompressible Navier-Stokes equations,” International Journal for Numerical Methods in Fluids, vol. 66, no. 4, pp. 486–508, 2011. View at Publisher · View at Google Scholar · View at Scopus
  16. M. Benzi and Z. Wang, “Analysis of augmented lagrangian-based preconditioners for the steady incompressible navier-stokes equations,” SIAM Journal on Scientific Computing, vol. 33, no. 5, pp. 2761–2784, 2011. View at Publisher · View at Google Scholar · View at Scopus
  17. M. Benzi and M. A. Olshanskii, “Field-of-values convergence analysis of augmented lagrangian preconditioners for the linearized navier-stokes problem,” SIAM Journal on Numerical Analysis, vol. 49, no. 2, pp. 770–788, 2011. View at Publisher · View at Google Scholar · View at Scopus
  18. H. C. Elman, A. Ramage, and D. J. Silvester, “IFISS: a Matlab toolbox for modelling incompressible flow,” ACM Transactions on Mathematical Software, vol. 33, no. 2, Article ID 1236469, 2007. View at Publisher · View at Google Scholar · View at Scopus
  19. P. R. Amestoy, T. A. Davis, and I. S. Duff, “An approximate minimum degree ordering algorithm,” SIAM Journal on Matrix Analysis and Applications, vol. 17, no. 4, pp. 886–905, 1996. View at Google Scholar · View at Scopus
  20. T. A. Davis, Direct Methods for Sparse Linear Systems, Society for Industrial and Applied Mathematics, Philadelphia, Pa, USA, 2006.