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

[Alp Kalpalp]

In FETI, system is replaced with a coarse problem of dual variables
(drastically smaller coarse problem size) and by using a projector more
well-conditioned system is obtained. Condition number is limited to
1+log(H/h)^2.
As the literature suggests, I need to apply projector on PCG. I tested
KSPDGMRES and it seems CG is more successful. So it seems my only way is to
implement my own variant of KSPCG. May I just copy the  files and
definitions related to KSPCG and rename all as KSPPCPG. And then I can make
the orthogonolization implementation similar to KSPDGMRES..

Jed, please warn me if this is a really hard task?

I dont want to put myself into a long journey of implementation :)

best regards,

On Sun, Dec 28, 2014 at 8:48 PM, Jed Brown <jed at jedbrown.org> wrote:

> Umut Tabak <u.tabak at tudelft.nl> writes:
> > 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,
>
> Ill-conditioning is a red herring.  For example, FMG can solve
> well-behaved problems with 1e12 condition number in one cycle (about 5
> "work units").  OTOH, very well-conditioned problems with eigenvalues
> encircling the origin converge extremely slowly (these are
> nonsymmetric).  Anyway, some SPD industrial problems see poor
> performance with AMG, BDDC, and similar otherwise-scalable methods due
> to discretization or physical features that elude the heuristics used to
> produce good coarse spaces.  Sometimes these problems can be formulated
> in more solver-friendly ways.  Other times, custom methods would be
> needed.  Or the methods could converge well, but only with high grid
> complexity (coarse spaces that do not decay in size fast enough).
>
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