[petsc-users] Initial Guess for KSP in SNES

[Derek Gaston]

I suppose that's a good point.

This came about because I happen to be solving linear problems right now -
and I'm just using KSP - but I'm still solving for an "update" as in a
Newton method.  So, naturally, I wanted to "predict" the update of that
linear problem each timestep.  That got me thinking about what we generally
choose as the initial guess for the KSP in SNES so I went looking.

I think the moral of the story here is, as per usual, making good guesses
for the solution of the nonlinear solve is a good idea. It obviously helps
Newton and it makes the initial guess of 0 for the solution of the update
also make more sense.

Also: I hadn't really considered the effect of an initial guess on a Krylov
solver before.  It's intuitively obvious that providing a good initial
guess helps Newton (for instance, guessing within the ball of
convergence)... but I haven't seen much work on how the initial guess
effects Krylov solvers before.  A bit of googling led me to this paper
which is interesting:
http://dodo.inm.ras.ru/vassilevski/wp-content/uploads/2015/01/jcp219_210-227.pdf
do
you know of another reference that is related?

Thanks for the response,
Derek

On Sun, Apr 29, 2018 at 11:54 AM Jed Brown <jed at jedbrown.org> wrote:

> Why do you want it to be an initial guess for the linear problem rather
> than for the nonlinear problem?
>
> I think you can use SNESSetUpdate() and in that function,
> SNESGetSolutionUpdate() which you can set to whatever you want the
> initial guess to be.
>
> Derek Gaston <friedmud at gmail.com> writes:
>
> > I'm interested in setting the initial guess for the first KSP solve in
> SNES
> > (used in a transient calculation) - and whether anyone thinks it could
> be a
> > good thing to do.
> >
> > I see some previous discussion on this from Jed and Matt here:
> >
> https://lists.mcs.anl.gov/mailman/htdig/petsc-users/2014-September/022779.html
> >
> https://lists.mcs.anl.gov/mailman/htdig/petsc-users/2014-September/022780.html
> >
> > I realize that the Newton solver is solving for the update... but that
> > doesn't necessarily mean that guessing 0 is the best plan.  For instance:
> > for fairly linear problems in time (or slightly nonlinear depending on
> how
> > you look at it!) it might be a good idea to guess the first update to be
> > the difference between the previous two time steps (or: more generally
> some
> > sort of "projected" update based on your time integration scheme).
> >
> > Indeed - for a perfectly linear problem in time (with constant dt) this
> > would yield a "perfect" guess for the linear solver and it would return
> > immediately.
> >
> > I suppose that if you use a "predictor" for predicting the guess for the
> > nonlinear system (which we often do - but not always)... then 0 for your
> > first update is probably a decent choice (what else would you choose?).
> > But if you're simply using the old timestep solution (which is what is
> > commonly done)... then that first update is more likely to look like the
> > difference between the last two timesteps than it looks like 0.
> >
> > Thoughts?
> >
> > Derek
>
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