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

[Jed Brown]

Alp Kalpalp <alpkalpalp at gmail.com> writes:

> Thanks for the answers,
>
> Please forgive me, I forgot to say that my stiffness matrix is not changing
> during time steps. I could not remember directly but just after a google
> search..I just hit this
>
> http://web.stanford.edu/group/frg/publications/recent/FETI-stoch.pdf
>
> please look around eq37
>
> My problem is not related to this random paper I found. But, I think I can
> find several others that shows the enhancing power of orthogonalization
> with successive directions when the system's behaviour is not changing
> rapidly. In my current sample case a gradually increasing force is applied
> to a linear system.

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.

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.
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