[dune-pdelab] Deflated CG

[Marian Piatkowski]

Hi Anne,


there is no deflated CG, neither in ISTL nor in PDELab. But maybe the 
following comment might also help.

Since you are solving problems with singular matrices, my question is:

Do you observe that the norm of the residual gets more likely stuck in 
the parallel case whereas in the sequential case the CG solver does 
converge.

If so, you could orthogonalize the corrections in CG against the null 
space of the matrix. But this requires of course a priori knowledge of 
the null space of your matrix (in particular an orthogonal basis with 
respect to the Euclidian scalar product). You can have a look at my code 
in order to see what needs to be changed inside the CG solver. 
Unfortunately I have only hard-coded this to the case of one-dimensional 
kernel spanned by the constant vector.


I have attached the file with the modified CG solver. The relevant code 
starts at line 74. Just search after 'if(singular)' inside this class.


Regards,

Marian



On 07/10/2017 09:59 PM, Anne Reinarz wrote:
>
> Hi everyone,
>
> I have a linear system I'm trying to solve with CG preconditioned with 
> AMG, but the operator has a kernel of dimension 6, so the norm of the 
> residual is very high and the stopping criterion doesn't seem to work. 
> I was wondering if other people have had similar problems. Is there is 
> a deflated preconditioned CG available, or something similar?
>
> Thanks for your help,
> Anne
>
>
>
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