[petsc-users] SNES: approximating the Jacobian with computed residuals?

[Peter Brune]

-snes_view would also be useful for basic santity checks.


On Tue, Apr 22, 2014 at 11:43 AM, Peter Brune <prbrune at gmail.com> wrote:

>
>
>
> On Tue, Apr 22, 2014 at 10:56 AM, Fischer, Greg A. <
> fischega at westinghouse.com> wrote:
>
>>
>>
>> *From:* Peter Brune [mailto:prbrune at gmail.com]
>> *Sent:* Tuesday, April 22, 2014 10:16 AM
>> *To:* Fischer, Greg A.
>> *Cc:* petsc-users at mcs.anl.gov
>> *Subject:* Re: [petsc-users] SNES: approximating the Jacobian with
>> computed residuals?
>>
>>
>>
>> On Tue, Apr 22, 2014 at 8:48 AM, Fischer, Greg A. <
>> fischega at westinghouse.com> wrote:
>>
>> Hello PETSc-users,
>>
>> I'm using the SNES component with the NGMRES method in my application.
>> I'm using a matrix-free context for the Jacobian and the
>> MatMFFDComputeJacobian() function in my FormJacobian routine. My
>> understanding is that this effectively approximates the Jacobian using the
>> equation at the bottom of Page 103 in the PETSc User's Manual. This works,
>> but the expense of computing two function evaluations in each SNES
>> iteration nearly wipes out the performance improvements over Picard
>> iteration.
>>
>>
>>
>> Try -snes_type anderson.  It's less stable than NGMRES, but requires one
>> function evaluation per iteration.  The manual is out of date.  I guess
>> it's time to fix that.  It's interesting that the cost of matrix assembly
>> and a linear solve is around the same as that of a function evaluation.
>>  Output from -log_summary would help in the diagnosis.
>>
>>
>>
>> I tried the –snes_type anderson option, and it seems to be requiring even
>> more function evaluations than the Picard iterations. I’ve attached
>> –log_summary output. This seems strange, because I can use the NLKAIN code (
>> http://nlkain.sourceforge.net/) to fairly good effect, and I’ve read
>> that it’s related to Anderson mixing. Would it be useful to adjust the
>> parameters?
>>
>
> If I recall correctly, NLKAIN is yet another improvement on Anderson
> Mixing.  Our NGMRES is what's in O/W and is built largely around being
> nonlinearly preconditionable with something strong like FAS.  What is the
> perceived difference in convergence? (what does -snes_monitor say?) Any
> multitude of tolerances may be different between the two methods, and it's
> hard to judge without knowing much, much more.  Seeing what happens when
> one changes the parameters is of course important if you're looking at
> performance.
>
> By Picard, you mean simple fixed-point iteration, right?  What constitutes
> a Picard iteration is a longstanding argument on this list and therefore
> requires clarification, unfortunately. :)  This (without linesearch) can be
> duplicated in PETSc with -snes_type nrichardson -snes_linesearch_type
> basic.  For a typical problem one must damp this with
> -snes_linesearch_damping <damping parameter>  That's what the linesearch is
> there to avoid, but this takes more function evaluations.
>
>
>>
>>
>> I’ve also attached –log_summary output for NGMRES. Does anything jump out
>> as being amiss?
>>
>
>       ##########################################################
>       #                                                        #
>       #                          WARNING!!!                    #
>       #                                                        #
>       #   This code was compiled with a debugging option,      #
>       #   To get timing results run ./configure                #
>       #   using --with-debugging=no, the performance will      #
>       #   be generally two or three times faster.              #
>       #                                                        #
>       ##########################################################
>
> Timing comparisons aren't reasonable with debugging on.
>
>
>>
>>
>>
>>
>> Based on my (limited) understanding of the Oosterlee/Washio SIAM paper
>> ("Krylov Subspace Acceleration of Nonlinear Multigrid..."), they seem to
>> suggest that it's possible to approximate the Jacobian with a series of
>> previously-computed residuals (eq 2.14), rather than additional function
>> evaluations in each iteration. Is this correct? If so, could someone point
>> me to a reference that demonstrates how to do this with PETSc?
>>
>>
>>
>> What indication do you have that the Jacobian is calculated at all in the
>> NGMRES method?  The two function evaluations are related to computing the
>> quantities labeled F(u_M) and F(u_A) in O/W.  We already use the Jacobian
>> approximation for the minimization problem (2.14).
>>
>>
>>
>> - Peter
>>
>>
>>
>> Thanks for the clarification.
>>
>>
>>
>> -Greg
>>
>>
>>
>>
>> Or, perhaps a better question to ask is: are there other ways of reducing
>> the computing burden associated with estimating the Jacobian?
>>
>> Thanks,
>> Greg
>>
>>
>>
>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20140422/787423a4/attachment.html>