[petsc-users] no decrease in iteration counts of KSPCG during time stepping

[Umut Tabak]

On 12/28/2014 07:12 PM, Jed Brown wrote:
> Alp Kalpalp <alpkalpalp at gmail.com> writes:
>
> Is the force moving or just increasing?  The idea with this class of
> methods is that you add a Galerkin coarse correction where the basis
> functions approximate some low-frequency eigenvectors of the system.
> The projection is relatively expensive in parallel, but could save
> iterations.  It's not "scalable" for many outlier eigenvalues because
> the projection space would get too big as the problem size is increased,
> but when combined with a decent-but-not-too-good preconditioner, could
> improve performance.
Well, I am following the discussion since it is also interesting for me.

I am not sure if it will help for future, but let me give an overview 
from my research experience:

As a poor engineer, my experience was with iterative methods on 
ill-conditioned problems, all the FE stiffness matrices are ill 
conditioned due to the multiplication of the gradient operators, 
especially the ones for thin structures encountered in vibroacoustics, 
or shell like structures for instance, and on these problems I could 
never get successful results with my tries even with the projections 
w.r.t. the previous vectors. Tim Davies has some kind of nice guidelines 
when to use iterative methods, I do not remember the links now but you 
should be able to find them easily, after reading them and trying more I 
did not continue more on that...

Preconditioner side: my experience was that one should be really lucky 
to get a good preconditioner which is really really rare, as mentioned, 
especially for ill-conditioned problems, almost impossible. If my 
condition number estimate is above, say, 1e4  1e5, I do not expect much 
from iterative methods, for SPD problems of course, my 2 cents, without 
theoretical details of Krylov subspace methods.

BR,
Umut
>
> You can implement this in the general case using PCCOMPOSITE+PCGALERKIN
> or with PCMG.  You can also use KSPDGMRES or KSPAGMRES (man page missing
> in the release -- I reactivated, but look at the code until it
> regenerates), which attempt to automatically build a space.
>
> http://www.mcs.anl.gov/petsc/petsc-dev/docs/manualpages/KSP/KSPDGMRES.html
>
> You could implement a deflated CG in a similar way if you want to
> automatically extract the deflation vectors from the CG iteration.