[petsc-users] SNESVI convergence spped

[Dmitry Karpeev]

It seems to me that the problem is that ultimately ALL of the degrees of
freedom are in the active set,
but they get added to it a few at a time -- and there may even be some
"chatter" there -- necessitating many SNESVI steps.
Could it be that the regularization makes things worse? When \epsilon \ll
1, the unconstrained solution is highly oscillatory, possibly further
exacerbating the problem. It's possible that it would be better if V just
diverged uniformly.  Then nearly all of the degrees of freedom would bump
up against the upper obstacle all at once.

Dmitry.

On Mon, Jan 16, 2012 at 8:05 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:

>
>  What do you get with -snes_vi_monitor   it could be it is taking a while
> to get the right active set.
>
>    Barry
>
> On Jan 16, 2012, at 6:20 PM, Ataollah Mesgarnejad wrote:
>
> > Dear all,
> >
> > I'm trying to use SNESVI to solve a quadratic problem with box
> constraints. My problem in FE context reads:
> >
> > (\int_{Omega} E phi_i phi_j + \alpha \epsilon dphi_i dphi_j dx) V_i -
> (\int_{Omega} \alpha \frac{phi_j}{\epsilon} dx) = 0 , 0<= V <= 1
> >
> > or:
> >
> > [A]{V}-{b}={0}
> >
> > here phi is the basis function, E and \alpha are positive constants, and
> \epsilon is a positive regularization parameter  in order of mesh
> resolution. In this problem we expect V  =1 a.e. and go to zero very fast
> at some places.
> > I'm running this on a rather small problem (<500000 DOFS) on small
> number of processors (<72). I expected SNESVI to converge in couple of
> iterations (<10) since my A matrix doesn't change, however I'm experiencing
> a slow convergence (~50-70 iterations). I checked KSP solver for SNES and
> it converges with a few iterations.
> >
> > I would appreciate  any suggestions or observations to increase the
> convergence speed?
> >
> > Best,
> > Ata
>
>
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