[petsc-users] Question regarding preconditioning in L-BFGS

[Michael White]

I may have exaggerated when I described the preconditioner as "good". All I
know about the preconditioner is that it helps. It is a very rough
approximation of the Jacobian. So I don't think I can just use the
preconditioner as a stand-in for the Jacobian.

As for using -snes_mf_operator, I doubt that would work. I'm minimizing the
energy of a large lattice with defects, and when I use a simplified form of
the energy, I still have to resort to Kahan summation to preserve enough
accuracy in the Jacobian to get the system to converge. For this reason, I
don't think a finite difference approximation of the Jacobian will work due
to the loss of precision already inherent in the calculation.

Best,
Michael


On Wed, Jul 1, 2015 at 5:43 AM, Matthew Knepley <knepley at gmail.com> wrote:

> On Wed, Jul 1, 2015 at 7:19 AM, Michael White <mrwhite at umn.edu> wrote:
>
>> Hello,
>>
>> I am not quite sure how to use the L-BFGS implementation in PETSc with a
>> preconditioner that approximates the Jacobian. As far as I understand it,
>> L-BFGS is like Newton's Method but doesn't require the user to input the
>> Jacobian matrix. However, for my application, I do have a good
>> preconditioner that approximates the Jacobian matrix. My question is where
>> to input such a preconditioner. I have 3 possible guesses about the correct
>> way to do it.
>>
>> 1. Use SNESSetJacobian to provide a function which computes the
>> preconditioner. I'm unsure if this information is even used though, since
>> L-BFGS builds its own approximation to the inverse Jacobian as it goes.
>>
>> 2. Use SNESQNSetScaleType with SNES_QN_SCALE_JACOBIAN to set my
>> preconditioner as an initial approximation to the Jacobian somehow?
>>
>
> This is the intent, but we have no tests of this in PETSc, so let me know
> if this works. Jed Brown and Peter Brune have a paper
> where they do this and it has the options they used.
>
>
>> 3. Use an SNESSetNPC with my preconditioner as a linear preconditioner?
>>
>> Anyone that could point me in the right direction would be greatly
>> appreciated.
>>
>
> Why are you using L-BFGS if you have a good Jacobian preconditioner? You
> could do Newton with that
> preconditioning matrix and MF application of the Jacobian.
>
>   Thanks,
>
>    Matt
>
>
>> Best regards,
>> Michael White
>>
>>
>>
>
>
> --
> 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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