[petsc-users] Simultaneously compute Residual+Jacobian in SNES

[Matthew Knepley]

On Fri, Dec 9, 2016 at 2:10 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:

>
> > On Dec 9, 2016, at 1:50 PM, Derek Gaston <friedmud at gmail.com> wrote:
> >
> > Oh man!  Sorry Barry!  I swear I looked around before I sent the email.
> I should have checked the FAQ a little more closely!
> >
> > I can understand the reasoning in the FAQ... but I still wonder if it
> might not be useful to provide all three options (Function, Jacobian,
> FunctionJacobian).  In my case I could fill in each one to do the right
> thing.  That way PETSc could call the "FunctionJacobian" one when it knew
> it needed both
>
>    Derek,
>
>       The code literally never knows if it will need a Jacobian following
> the function evaluation, yes at the first function evaluation it will need
> the Jacobian unless the function norm is sufficiently small but after that
> it is only a question of probabilities (which it can't know) whether it
> will need the Jacobian.
>
> > (by default that could just farm out to the individual calls).  But you
> guys have definitely thought a lot more about this than I have.
> >
> > So, do you still recommend what's suggested in the FAQ?  Save off the
> Jacobian computation during the residual computation and then use that when
> SNES asks for a Jacobian?
>
>    Yes, try it. I think you can get away with simply putting the new
> Jacobian matrix values into the same Jacobian matrix that is regularly used
> so there is no need to "stash the values" somewhere else and copy them over
> later.
>
>    I'd be interested in hearing how the performance works out, compute
> always or compute only when requested.


Can anyone write down a simple model for a concrete algorithm where this is
more efficient? I would like to see the high level reasoning.

  Thanks,

    Matt


>
>   Barry
>
> >  In the case of automatic differentiation this could make a pretty huge
> difference in time...
> >
> > Derek
> >
> > On Fri, Dec 9, 2016 at 1:49 PM Barry Smith <bsmith at mcs.anl.gov> wrote:
> >
> >   Sorry the title in the FAQ is a bit tongue-in-check.
> >
> >   http://www.mcs.anl.gov/petsc/documentation/faq.html#functionjacobian
> >
> >
> > > On Dec 9, 2016, at 12:45 PM, Derek Gaston <friedmud at gmail.com> wrote:
> > >
> > > Is there a way to tell SNES to simultaneously compute both the
> residual and the Jacobian in one callback?
> > >
> > > My code can compute both simultaneously and it will be more efficient
> (think FE where you can reuse the shape-functions, variables, material
> properties, etc. for both residual and Jacobian computation).  In addition,
> I also have automatic differentiation as an option which _definitely_
> computes both efficiently (and actually computes residuals, by themselves,
> much slower).
> > >
> > > I was thinking that I may just save off the Jacobian whenever the
> initial residual computation is asked for by SNES... and then just return
> that Jacobian when SNES asks for it.  This may be a bit dicey though as
> SNES can ask for residual computations at many different points during the
> solve.
> > >
> > > Thanks for any help!
> > >
> > > Derek
> >
>
>


-- 
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
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