[petsc-users] SNES + linesearch hackery?

[Matthew Knepley]

On Thu, Mar 24, 2016 at 3:06 PM, Andrew McRae <A.T.T.McRae at bath.ac.uk>
wrote:

> On 24 March 2016 at 19:49, Barry Smith <bsmith at mcs.anl.gov> wrote:
>
>>
>> > On Mar 24, 2016, at 2:41 PM, Andrew McRae <A.T.T.McRae at bath.ac.uk>
>> wrote:
>> >
>> > Apologies, in the end it seems this was more of a Firedrake question:
>> with the help of Lawrence Mitchell, I now believe I should simply intercept
>> SNESFormFunction().
>> >
>> > On 24 March 2016 at 17:39, Barry Smith <bsmith at mcs.anl.gov> wrote:
>> >
>> > > On Mar 24, 2016, at 10:18 AM, Andrew McRae <A.T.T.McRae at bath.ac.uk>
>> wrote:
>> > >
>> > > I have a finite element discretisation of the following nonlinear
>> equation:
>> > >
>> > > m*(phi_xx * phi_yy - phi_xy^2) = const,
>> > >
>> > > solving for phi.  Unfortunately, the function m depends on phi in a
>> complicated way -- let's assume I need to call my own function to handle
>> this.
>> >
>> >   Andrew
>> >
>> >    So you are actually solving
>> >
>> >   m(phi)*(phi_xx * phi_yy - phi_xy^2) - const = 0
>> >
>> >   with finite elements for phi?
>> >
>> >
>> >     What are you providing for a Jacobian?
>> >
>> > The Jacobian I give treats m as being independent of phi, so just
>> whatever you get from linearising det(Hessian(phi)).
>>
>>   Ahh, a Picard iteration :-)
>>
>
> Not quite, I think.
>
> Ah, that should have read "so just m*(whatever you get from
> linearising...)", and I was updating m between nonlinear iterations :)
>

I think Barry is right. You can look at it this way. You froze a portion of
your system, took the Jacobian of the rest, and
used that for the step, then updated the frozen part. That is what lots of
people call a Picard step.

  Matt


>
>>
>> >
>> >
>> >
>> > >
>> > > I'm using PETSc's SNES  in Python via petsc4py, within the wider
>> environment of the software Firedrake.
>> > >
>> > > Currently I'm hacking in the m update (and various output
>> diagnostics) by writing a Python function "fakemonitor" and calling
>> snes.setMonitor(fakemonitor).  This allows me to update m each nonlinear
>> iteration.
>> >
>> >     Hmm, I don't understand this. It sounds like you are passing
>> (phi_xx * phi_yy - phi_xy^2) or something to SNES as the
>> SNESFormFunction()? Why is this? Why not pass the entire function to SNES?
>> >
>> > I was passing in m(phi^n)(phi_xx * phi_yy - phi_xy^2) - const, i.e., m
>> was effectively frozen from the last nonlinear iteration.  As stated above,
>> I think it's as simple as arranging for m to be updated whenever
>> SNESFormFunction() is called, which involves hacking Firedrake code but not
>> PETSc code.
>> >
>> > Thanks,
>> > Andrew
>> >
>> >
>> >   Barry
>> >
>> > >
>> > > While this is better than nothing, there's still some problems: if I
>> use e.g. snes_linesearch_type: "l2", the fnorms for lambda = 1.0, 0.5 and
>> 0.0 are calculated without updating m, and so the step length taken is
>> (seemingly) far from optimal.  I tried adding a damping parameter, but all
>> this does is change the lambdas used to generate the quadratic fit; it
>> doesn't actually make the step length smaller.
>> > >
>> > > Is there some cleaner way to do what I want, perhaps by intercepting
>> the fnorm calculation to update m, rather than abusing a custom monitor
>> routine?
>> > >
>> > > Thanks,
>> > > Andrew
>> >
>> >
>>
>>
>


-- 
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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