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A new preconditioner for the Oseen equations

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • A. Wathen

    (Oxford University, Computing Laboratory)

  • D. Loghin

    (Oxford University, Computing Laboratory)

  • D. Kay

    (Sussex University, School of Mathematical Sciences)

  • H. Elman

    (University of Maryland, Department of Computer Science and Institute of Advanced Computer Studies)

  • D. Silvester

    (UMIST, Department of Mathematics)

Abstract

Summary We describe a preconditioner for the linearised incompressible Navier-Stokes equations (the Oseen equations) which requires as components a preconditioner/solver for a discrete Laplacian and for a discrete advection-diffusion operator. With this preconditioner, convergence of an iterative method such as GMRES is independent of the mesh size and depends only mildly on the viscosity parameter (the inverse Reynolds number). Thus when the component preconditioner/solvers are effective on their respective subproblems (as one expects with an appropriate multigrid cycle for instance)a fast Oseen solver results.

Suggested Citation

  • A. Wathen & D. Loghin & D. Kay & H. Elman & D. Silvester, 2003. "A new preconditioner for the Oseen equations," Springer Books, in: Franco Brezzi & Annalisa Buffa & Stefania Corsaro & Almerico Murli (ed.), Numerical Mathematics and Advanced Applications, pages 979-988, Springer.
    • Handle: RePEc:spr:sprchp:978-88-470-2089-4_89
    DOI: 10.1007/978-88-470-2089-4_89
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