The Mathematical Institute, University of Oxford, Eprints Archive

Analysis of preconditioned Picard iterations for the Navier-Stokes equations

Loghin, Daniel (2001) Analysis of preconditioned Picard iterations for the Navier-Stokes equations. Technical Report. Unspecified. (Submitted)

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Abstract

Mixed finite element formulations of fluid flow problems lead to large systems of equations of saddle-point type for which iterative solution methods are mandatory for reasons of efficiency. A successful approach in the design of solution methods takes into account the structure of the problem; in particular, it is well-known that an efficient solution can be obtained if the associated Schur complement problem can be solved efficiently and robustly. In this work we analyze a preconditioner for the Schur complement for the Oseen problem which was introduced in Numerical Analysis Report No. 99/06 We show that the spectrum of the preconditioned system is independent of the mesh parameter; moreover, we demonstrate that the number of GMRES iterations grows like the square-root of the Reynolds number for steady-state problems, while for time-dependent problems this dependence becomes negligible. In both the steady-state and time-dependent case the performance is mesh-independent.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1241
Deposited By:Lotti Ekert
Deposited On:20 May 2011 09:19
Last Modified:20 May 2011 09:19

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