Loghin, Daniel (2001) Analysis of preconditioned Picard iterations for the NavierStokes 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 saddlepoint 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 wellknown 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 squareroot of the Reynolds number for steadystate problems, while for timedependent problems this dependence becomes negligible. In both the steadystate and timedependent case the performance is meshindependent.
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 08:19 
Last Modified:  29 May 2015 18:56 
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