[Dune] [#928] breakdown of BiCGSTAB

[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

-- 
Markus Blatt, Interdisciplinary Center for Scientific Computing,
University Heidelberg, Im Neuenheimer Feld 368, D-69120 Heidelberg

'Mathematics knows no races or geographic boundaries; for
mathematics, the cultural world is one country' - David Hilbert