[petsc-users] Debugging SNES when "everything" looks okay

[Matthew Knepley]

On Tue, Aug 21, 2018 at 10:00 PM Ellen M. Price <ellen.price at cfa.harvard.edu>
wrote:

> Hi PETSc users,
>
> I'm having trouble applying SNES to a new problem I'm working on. I'll
> try to be as complete as possible but can't post the full code because
> it's ongoing research and is pretty long anyway.
>
> The nonlinear problem arises from trying to solve a set of two coupled
> ODEs using a Galerkin method. I am using Mathematica to generate the
> objective function to solve and the Jacobian, so I *think* I can rule
> out human error on that front.
>
> There are four things I can easily change:
>
> - number of DMDA grid points N (I've tried 100 and 1000)
> - preconditioner (I've tried LU and SVD, LU appears to work better, and
> SVD is too slow for N = 1000)
> - linear solver (haven't played with this much, but sometimes smaller
> tolerances work better)
> - nonlinear solver (what I'm having trouble with)
>
> Trying different solvers should, as far as I'm aware, give comparable
> answers, but that's not the case here. NEWTONTR works best of the ones
> I've tried, but I'm suspicious that the function value barely decreases
> before SNES "converges" -- and none of the options I've tried changing
> seem to affect this, as it just finds another reason to converge without
> making any real progress. For example:
>
>   0 SNES Function norm 7.197788479418e+00
>     0 KSP Residual norm 1.721996766619e+01
>     1 KSP Residual norm 5.186021549059e-14
>   Linear solve converged due to CONVERGED_STEP_LENGTH iterations 1
>

This makes no sense. LU should converge due to atol or rtol. Send the
output of

  -snes_view -snes_monitor -snes_converged_reason
-ksp_monitor_true_residual -ksp_converged_reason

  Thanks,

    Matt


>   1 SNES Function norm 7.197777674987e+00
>     0 KSP Residual norm 3.296112185897e+01
>     1 KSP Residual norm 2.713415432045e-13
>   Linear solve converged due to CONVERGED_STEP_LENGTH iterations 1
> .....
>  50 SNES Function norm 7.197376803542e+00
>     0 KSP Residual norm 6.222518656302e+02
>     1 KSP Residual norm 9.630659996504e-12
>   Linear solve converged due to CONVERGED_STEP_LENGTH iterations 1
>  51 SNES Function norm 7.197376803542e+00
> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 50
>
> I've tried everything I can think of and the FAQ suggestions, including
> non-dimensionalizing the problem; I observe the same behavior either
> way. The particularly strange thing I can't understand is why some of
> the SNES methods fail outright, after just one iteration (NCG, NGMRES,
> and others) with DIVERGED_DTOL. Unless I've misunderstood, it seems
> like, for the most part, I should be able to substitute in one method
> for another, possibly adjusting a few parameters along the way.
> Furthermore, the default method, NEWTONLS, diverges with
> DIVERGED_LINE_SEARCH, which I'm not sure how to debug.
>
> So the only viable method is NEWTONTR, and that doesn't appear to
> "really" converge. Any suggestions for further things to try are
> appreciated. My current options are:
>
> -pc_type lu -snes_monitor -snes_converged_reason -ksp_converged_reason
> -snes_max_it 10000 -ksp_monitor -snes_type newtonls
>
> Thanks in advance,
> Ellen Price
>


-- 
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

https://www.cse.buffalo.edu/~knepley/ <http://www.caam.rice.edu/~mk51/>
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