Non repeatability issue

Matthew Knepley knepley at
Tue Mar 18 08:00:40 CDT 2008

To me this looks like

  1) You have way too many Newton steps. Newton is quadratically
convergent, so if
      you have 100+ steps, it means you are very very far from the
solution when you
      begin. In this region, Newton is a really bad algorithm and can
be very very
      sensitive to perturbations. I would never expect it to be
reproducible. From the
      well-known fracint demo, it can be chaotic.

  2) I would also question whether the system is actually stable.
Instability can result
      in occasional divergence based upon small perturbations.

Thus, I am not sure you are asking the correct question with this
solve. I don't think
reproducible Newton over 100s of steps makes sense theoretically. Maybe Barry
thinks differently.


On Tue, Mar 18, 2008 at 5:57 AM, Aldo Bonfiglioli
<aldo.bonfiglioli at> wrote:
> >
>  > 1)    Have you made runs where you require, say -ksp_rtol 1.e-12 to
>  > eliminate the effects of
>  > not solving the linear systems accurately?
>  I have performed two runs with ksp_rtol = 1.e-12. The relevant plots are
>  enclosed
>  where comparisons are made with PETSc's default for ksp_rtol.
>  In one of these two runs Newton even diverges.
>  It should however be mentioned that
>  at least for some Newton steps, the linear solver does not meet the
>  convergence criterion in 2000 linear iterations (I reduced the default).
>  > I have added the  argument -vecscatter_reproduce
>  > that will cause the receives to always be processed in the same order
>  > (though order or
>  > operations in the MPI reductions may still result in slightly
>  > different convergence histories.)
>  >
>  >   Hope this helps clear things up,
>  I am not sure "-vecscatter_reproduce " has changed the situation much.
>  Out of 4 subsequent runs, 2 converge
>  while 2 enter a limit cycle I had not seen previously
>  (I mean without the -vecscatter_reproduce option).
>  The initial solution is the same as that shown in the other plot.
>  Aldo
>  --
>  Dr. Aldo Bonfiglioli
> di Ingegneria e Fisica dell'Ambiente (DIFA)
>  Universita' della Basilicata
>  V.le dell'Ateneo lucano, 10 85100 Potenza ITALY
>  tel:+39.0971.205203 fax:+39.0971.205160

What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which
their experiments lead.
-- Norbert Wiener

More information about the petsc-users mailing list