[Dune] [#928] breakdown of BiCGSTAB

[Andreas Lauser]

Hi All,

I might be wrong (In this case I appologize for the noise), but I always 
thought that BiCG(Stab) reduces to CG in the symmetric positive definite case. 
If this is true, then the breakdown of BiCGStab but not CG indicates a problem 
with the ISTL implementation of BiCGStab, right?

cheers
  Andreas

Am Donnerstag, 9. Juni 2011, 14:44:52 schrieb Markus Blatt:
> Hi,
> 
> maybe my initial answer was not clear enough.
> 
> On Thu, Jun 09, 2011 at 02:14:05PM +0200, Bernd Flemisch wrote:
> > thank you for your answer. Although you apparently think that my
> > answer is not interesting since you already closed this task, I
> > provide it here anyway.
> 
> I closed it because with my suggested initial guess it works!
> 
> > This matrix and right hand side are coming from a to my knowledge
> > correct CVFE discretization of a simple diffusion equation on the
> > unit square discretized with 8x4 rectangular elements. Dirichlet BCs
> > on top and bottom, Neumann zero left and right. The solution of the
> > equation system is the physically correct one, meaning constant in x
> > and linear in y direction.
> > 
> > You are somehow right about suggesting a different right hand side.
> > The unusual form is coming from the fact that our Dirichlet BCs are
> > implemented a bit differently leading to 1's and 2's on the
> > diagonals in the original example. I changed that in the newly
> > attached example with only 1's on the Dirichlet diagonals and your
> > suggested rhs. BiCGSTAB still fails.
> 
> Actually I suggested to change the initial guess by incorporating the
> already known Dirichlet values into it. This seems fair. (I changed x
> and not b and used your original matrix!) This approach worked for me
> and somehow makes sense, doesn't it?
> 
> > Matlab's bicgstab works.
> 
> Using the same linear system, right hand side, initial guess and
> preconditioner? (Or are the Dirichlet Boundaries not represented as
> dofs?) Then they maybe use same look ahead techniques to
> prevent the breakdown. As I do not have Matlab I can only guess this.
> 
> Of course incorporating  such techniques would be nice for ISTL, too?
> Maybe filing another feature request is a good idea.
> 
> 
> Cheers,
> 
> Markus



-- 
Andreas Lauser
Lehrstuhl für Hydromechanik und Hydrosystemmodellierung
Universität Stuttgart - Institut für Wasserbau
Pfaffenwaldring 61
D-70569 Stuttgart
Tel: (+49) 0711/ 685-64719
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e-mail: andreas.lauser at iws.uni-stuttgart.de