User menu

Analysis of preconditioned iterative solvers for incompressible flow problems

Bibliographic reference Melchior, Samuel ; Legat, Vincent ; Van Dooren, Paul ; Wathen, A. J.. Analysis of preconditioned iterative solvers for incompressible flow problems. In: International Journal for Numerical Methods in Fluids, Vol. 68, p. 269-286
Permanent URL
  1. Lipnikov K., Vassilevski Yu., Parallel adaptive solution of the Stokes and Oseen problems on unstructured 3D meshes, Parallel Computational Fluid Dynamics 2003 (2004) ISBN:9780444516121 p.153-161, 10.1016/b978-044451612-1/50020-2
  2. Olshanskii Maxim A., A low order Galerkin finite element method for the Navier–Stokes equations of steady incompressible flow: a stabilization issue and iterative methods, 10.1016/s0045-7825(02)00513-3
  3. Quarteroni Alfio, Saleri Fausto, Veneziani Alessandro, Factorization methods for the numerical approximation of Navier–Stokes equations, 10.1016/s0045-7825(99)00192-9
  4. Benzi Michele, Golub Gene H., Liesen Jörg, Numerical solution of saddle point problems, 10.1017/s0962492904000212
  5. Elman, Finite Elements and Fast Iterative Solvers (2005)
  6. Turek Stefan, Efficient Solvers for Incompressible Flow Problems, ISBN:9783642635731, 10.1007/978-3-642-58393-3
  7. Benzi Michele, Olshanskii Maxim A., An Augmented Lagrangian‐Based Approach to the Oseen Problem, 10.1137/050646421
  8. de Niet A. C., Wubs F. W., Two preconditioners for saddle point problems in fluid flows, 10.1002/fld.1401
  9. Peters Jörg, Reichelt Volker, Reusken Arnold, Fast Iterative Solvers for Discrete Stokes Equations, 10.1137/040606028
  10. ur Rehman M., Vuik C., Segal G., A comparison of preconditioners for incompressible Navier-Stokes solvers, 10.1002/fld.1684
  11. Balay Satish, Gropp William D., McInnes Lois Curfman, Smith Barry F., Efficient Management of Parallelism in Object-Oriented Numerical Software Libraries, Modern Software Tools for Scientific Computing (1997) ISBN:9781461273684 p.163-202, 10.1007/978-1-4612-1986-6_8
  12. Comblen Richard, Legrand Sébastien, Deleersnijder Eric, Legat Vincent, A finite element method for solving the shallow water equations on the sphere, 10.1016/j.ocemod.2008.05.004
  13. Hanert Emmanuel, Roux Daniel Y. Le, Legat Vincent, Deleersnijder Eric, An efficient Eulerian finite element method for the shallow water equations, 10.1016/j.ocemod.2004.06.006
  14. White Laurent, Legat Vincent, Deleersnijder Eric, Tracer Conservation for Three-Dimensional, Finite-Element, Free-Surface, Ocean Modeling on Moving Prismatic Meshes, 10.1175/2007mwr2137.1
  15. Chiang T. P., Sheu W. H., Hwang Robert R., Effect of Reynolds number on the eddy structure in a lid-driven cavity, 10.1002/(sici)1097-0363(19980315)26:5<557::aid-fld638>;2-r
  16. Povitsky Alex, Three-dimensional flow in cavity at yaw, 10.1016/
  17. Cahouet J., Chabard J.-P., Some fast 3D finite element solvers for the generalized Stokes problem, 10.1002/fld.1650080802
  18. Gresho, Incompressible Flow and the Finite Element Method (1998)
  19. Kay David A., Gresho Philip M., Griffiths David F., Silvester David J., Adaptive Time-Stepping for Incompressible Flow Part II: Navier–Stokes Equations, 10.1137/080728032
  20. Simo J.C., Armero F., Unconditional stability and long-term behavior of transient algorithms for the incompressible Navier-Stokes and Euler equations, 10.1016/0045-7825(94)90042-6
  21. Paige C. C., Saunders M. A., Solution of Sparse Indefinite Systems of Linear Equations, 10.1137/0712047
  22. Brandt Achi, Algebraic multigrid theory: The symmetric case, 10.1016/0096-3003(86)90095-0
  23. Ruge J. W., Stüben K., 4. Algebraic Multigrid, Multigrid Methods (1987) ISBN:9781611971880 p.73-130, 10.1137/1.9781611971057.ch4
  24. Henson Van Emden, Yang Ulrike Meier, BoomerAMG: A parallel algebraic multigrid solver and preconditioner, 10.1016/s0168-9274(01)00115-5
  25. Babuška Ivo, The finite element method with Lagrangian multipliers, 10.1007/bf01436561
  26. Brezzi, RAIRO Analyse Numerique, 8, 129 (1974)
  27. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow (1969)
  28. Murphy Malcolm F., Golub Gene H., Wathen Andrew J., A Note on Preconditioning for Indefinite Linear Systems, 10.1137/s1064827599355153
  29. Axelsson, Finite Element Solution of Boundary Value Problems (1984)
  30. Rusten Torgeir, Winther Ragnar, A Preconditioned Iterative Method for Saddlepoint Problems, 10.1137/0613054
  31. Silvester David, Wathen Andrew, Fast Iterative Solution of Stabilised Stokes Systems Part II: Using General Block Preconditioners, 10.1137/0731070
  32. Wathen Andrew, Silvester David, Fast Iterative Solution of Stabilised Stokes Systems. Part I: Using Simple Diagonal Preconditioners, 10.1137/0730031
  33. Hestenes M.R., Stiefel E., Methods of conjugate gradients for solving linear systems, 10.6028/jres.049.044
  34. Saad Youcef, Schultz Martin H., GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems, 10.1137/0907058
  35. Trefethen, Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators (2005)
  36. Wathen Andy, Preconditioning and convergence in the right norm, 10.1080/00207160701355961
  37. Kay David, Loghin Daniel, Wathen Andrew, A Preconditioner for the Steady-State Navier--Stokes Equations, 10.1137/s106482759935808x
  38. Elman, Electronic Transactions on Numerical Analysis, 35, 257 (2009)
  39. Varga, Prentice-Hall: Englewood Cliffs, NJ, 1962 (2000)
  40. Wathen, Electronic Transactions on Numerical Analysis, 34, 125 (2009)
  41. Wathen A. J., Realistic Eigenvalue Bounds for the Galerkin Mass Matrix, 10.1093/imanum/7.4.449