[petsc-users] Initial Guess for KSP in SNES

[Stefano Zampini]

For linear time dependent problems you can try KSPGUESSFISCHER and
KSPGUESSPOD, that project the linear system on a lower dimensional
manifold. Note that there are also integrators, like bdf, that already
computed a fairly good initial guess for Newton.

Il Dom 29 Apr 2018, 21:14 Derek Gaston <friedmud at gmail.com> ha scritto:

> 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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