[Dune] [#928] breakdown of BiCGSTAB

Bernd Flemisch bernd at iws.uni-stuttgart.de
Thu Jun 9 14:14:05 CEST 2011

Hey Markus,

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.

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.

Matlab's bicgstab works.

This is a boiled down simple example, and of course I 
could use CG here. I might not for more complex problems 
where I have to rely on BiCGSTAB or GMRes.

Thanks for maybe taking one more look. Kind regards

On Thu, 09 Jun 2011 11:39:54 +0200
  Dune <flyspray at dune-project.org> wrote:
> The following task has a new comment added:
>FS#928 - breakdown of BiCGSTAB
> User who did this - Markus Blatt (mblatt)
> ----------
> Does your right hand side make sense from the physics of 
>the problem.
> Whenever this happened to us, the discretisation was 
>wrong. Most often the left and right hand side are not 
>compatible in terms of boundary conditions if breakdowns 
> try e.g. X=0; x[0:8] = -1e+05; which makes more sense 
>and satisfies BiCGSTAB!
> With BiCGStab breakdowns may occur. But this is rather a 
>problem of the algorithm than our implementation.
> If CG works, you should therefore use it.
> Did you also check bicgstab in matlab?
> ----------
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Bernd Flemisch                     phone: +49 711 685 
IWS, Universitaet Stuttgart          fax: +49 711 685 
Pfaffenwaldring 61        email: 
bernd at iws.uni-stuttgart.de
D-70569 Stuttgart        url: 
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