Relaxed ILU Preconditioning for the CG Solution of a Singular Boundary Value Problem for Pressure

  • Vincent A. Barker
  • Bo Gervang
Part of the Notes on Numerical Fluid Mechanics (NNFM) book series (NNFM, volume 29)


A splitting technique for solving the incompressible Navier-Stokes equations, whereby operations on pressure and velocity are decoupled, leads to a second-order singular boundary value problem for the determination of pressure. A finite volume discretization based on a nonuniform grid is applied to this problem, producing a linear system of equations whose coefficient matrix is symmetric positive semidefinite. We give an account of our experience with solving this system by the conjugate gradient method with relaxed ILU preconditioning. Particular attention is given to the effect of the nonuniformity of the grid.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    AXELSSON, O., BARKER, V.A.: “Finite Element Solution of Boundary Value Problems”, Academic Press, Orlando, Florida, 1984.zbMATHGoogle Scholar
  2. [2]
    AXELSSON, O., LINDSKOG, G.: “On the eigenvalue distribution of a class of preconditioning methods”, Numer. Math., 48 (1986) pp. 479–498.CrossRefzbMATHMathSciNetGoogle Scholar
  3. [3]
    NOTAY, Y.: “Incomplete factorization of singular linear systems”, BIT, 29 (1989) pp. 682–702.CrossRefzbMATHMathSciNetGoogle Scholar
  4. [4]
    NOTAY, Y. : “Solving positive (semi)definite linear systems by preconditioned iterative methods”, in Preconditioned Conjugate Gradient Methods, O. Axelsson and L. Kolotilina, eds., LNiM No.1457 pp. 105–125, Springer Verlag, 1990.CrossRefGoogle Scholar
  5. [5]
    WILKINSON, J.H.: “The Algebraic Eigenvalue Problem”, Clarendon Press, Oxford, 1965.zbMATHGoogle Scholar

Copyright information

© Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden 1993

Authors and Affiliations

  • Vincent A. Barker
    • 1
  • Bo Gervang
    • 2
  1. 1.Institute for Numerical AnalysisTechnical University of DenmarkLyngbyDenmark
  2. 2.Department of Fluid MechanicsTechnical University of DenmarkLyngbyDenmark

Personalised recommendations