Convergence Analysis of GMRES for a ConvectionDiffusion Model Problem
Jörg Liesen (TU Berlin)
(joint work with Zdenek Strakos, Academy of Sciences of the Czech Republic)
When GMRES is applied to discretized convectiondiffusion 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 wellknown model problem discretized via
the streamlinediffusion 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.
