21st GAMM-Seminar Leipzig on
Robust Fast Solvers

Max-Planck-Institute for Mathematics in the Sciences
Inselstr. 22-26, D-04103 [O->]Leipzig
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  21st GAMM-Seminar
January, 26th-28th, 2005
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  Abstract Jörg Liesen, Fri, 13.00-13.20 Previous Contents Next  
  Convergence Analysis of GMRES for a Convection-Diffusion Model Problem
Jörg Liesen (TU Berlin)

(joint work with Zdenek Strakos, Academy of Sciences of the Czech Republic)

When GMRES is applied to discretized convection-diffusion problems, it often exhibits an initial period of slow convergence followed by a faster decrease of the residual norms. For certain model problems several approaches were made to understand this behavior. However, the analyses are typically based on the matrix of the discretized system and they do not take into account any influence of the right hand side (boundary conditions). Therefore they cannot explain the length of the initial period which depends on the right hand side.

We will concentrate on a well-known model problem discretized via the streamline-diffusion finite element method. Instead of the eigendecomposition of the system matrix we use the simultaneous diagonalization of the matrix blocks to offer an explanation of the GMRES convergence behavior. We show how the initial period of slow convergence is related to the boundary conditions and address the question why the convergence in the second stage accelerates.


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Last updated:
28.01.2005 Impressum
Concept, Design and Realisation
[O->]Jens Burmeister (Uni Kiel), Kai Helms (MPI Leipzig)
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