[petsc-users] SNESVI convergence spped

[Dmitry Karpeev]

I think looking at the output of -snes_vi_monitor, as Barry suggested,
would be useful to see what really is going on.
What initial guess are you using?  If you initialize V = 1 then whether a
degree of freedom belongs to the  active set
or not will depend only on the sign of the residual there.  I imagine that
only a few dofs will be driven away from the box
boundary by a large E-term?

Dmitry.

On Mon, Jan 16, 2012 at 8:49 PM, Blaise Bourdin <bourdin at lsu.edu> wrote:

> Hi,
>
> Ata and I are working together on this. The problem he describes is 1/2 of
> the iteration of our variational fracture code.
> In our application, E is position dependant, and typically becomes very
> large along very thin bands with width of the order of epsilon in the
> domain. Essentially, we expect that V will remain exactly equal to 1 almost
> everywhere, and will transition to 0 on these bands. Of course, we are
> interested in the limit as epsilon goes to 0.
>
> If the problem indeed is that it takes many steps to add the degrees of
> freedom. Is there any way to initialize manually the list of active
> constraints? To give you an idea, here is a link to a picture of the type
> of solution we expect. blue=1
> https://www.math.lsu.edu/~bourdin/377451-0000.png
>
> Blaise
>
>
>
> 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
>>
>>
>
>  --
> Department of Mathematics and Center for Computation & Technology
> Louisiana State University, Baton Rouge, LA 70803, USA
> Tel. +1 (225) 578 1612, Fax  +1 (225) 578 4276
> http://www.math.lsu.edu/~bourdin
>
>
>
>
>
>
>
>
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