[petsc-users] Newton LS - better results on single processor

Thu Nov 9 15:33:38 CST 2017

Hi Stefano - when I referred to the iterations, I was trying to point out
that my method solves a series of nonlinear systems, with the solution to
the first problem being used to initialize the state vector for the second
problem, etc.  The reason I mentioned that was I thought perhaps I can
expect the residuals from single process solve to differ from the residuals
from multiprocess solve by a very small amount, say machine precision or
the tolerance of the KSP/SNES, that would be fine normally.  But, if there
is a possibility that those differences are somehow amplified by each of
the iterations (solution->initial state), that could explain what I see.

I agree that it is more likely that I have a bug in my code but I'm having
trouble finding it.

I ran a small problem with -pc_type redundant -redundant_pc_type lu, as you
suggested.  What I think is the relevant portion of the output is here
(i.e. there are small differences in the KSP residuals and SNES residuals):

-n 1, first "iteration" as described above:

  0 SNES Function norm 6.053565720454e-02

    0 KSP Residual norm 4.883115701982e-05

    0 KSP preconditioned resid norm 4.883115701982e-05 true resid norm
6.053565720454e-02 ||r(i)||/||b|| 1.000000000000e+00

    1 KSP Residual norm 8.173640409069e-20

    1 KSP preconditioned resid norm 8.173640409069e-20 true resid norm
1.742143029296e-16 ||r(i)||/||b|| 2.877879104227e-15

  Linear solve converged due to CONVERGED_RTOL iterations 1

      Line search: Using full step: fnorm 6.053565720454e-02 gnorm
2.735518570862e-07

  1 SNES Function norm 2.735518570862e-07

    0 KSP Residual norm 1.298536630766e-10

    0 KSP preconditioned resid norm 1.298536630766e-10 true resid norm
2.735518570862e-07 ||r(i)||/||b|| 1.000000000000e+00

    1 KSP Residual norm 2.152782096751e-25

    1 KSP preconditioned resid norm 2.152782096751e-25 true resid norm
4.755555202641e-22 ||r(i)||/||b|| 1.738447420279e-15

  Linear solve converged due to CONVERGED_RTOL iterations 1

      Line search: Using full step: fnorm 2.735518570862e-07 gnorm
1.917989238989e-17

  2 SNES Function norm 1.917989238989e-17

Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 2

-n 2, first "iteration" as described above:

  0 SNES Function norm 6.053565720454e-02

    0 KSP Residual norm 4.883115701982e-05

    0 KSP preconditioned resid norm 4.883115701982e-05 true resid norm
6.053565720454e-02 ||r(i)||/||b|| 1.000000000000e+00

    1 KSP Residual norm 1.007084240718e-19

    1 KSP preconditioned resid norm 1.007084240718e-19 true resid norm
1.868472589717e-16 ||r(i)||/||b|| 3.086565300520e-15

  Linear solve converged due to CONVERGED_RTOL iterations 1

      Line search: Using full step: fnorm 6.053565720454e-02 gnorm
2.735518570379e-07

  1 SNES Function norm 2.735518570379e-07

    0 KSP Residual norm 1.298536630342e-10

    0 KSP preconditioned resid norm 1.298536630342e-10 true resid norm
2.735518570379e-07 ||r(i)||/||b|| 1.000000000000e+00

    1 KSP Residual norm 1.885083482938e-25

    1 KSP preconditioned resid norm 1.885083482938e-25 true resid norm
4.735707460766e-22 ||r(i)||/||b|| 1.731191852267e-15

  Linear solve converged due to CONVERGED_RTOL iterations 1

      Line search: Using full step: fnorm 2.735518570379e-07 gnorm
1.851472273258e-17

  2 SNES Function norm 1.851472273258e-17

-n 1, final "iteration":

  0 SNES Function norm 9.695669610792e+01

    0 KSP Residual norm 7.898912593878e-03

    0 KSP preconditioned resid norm 7.898912593878e-03 true resid norm
9.695669610792e+01 ||r(i)||/||b|| 1.000000000000e+00

    1 KSP Residual norm 1.720960785852e-17

    1 KSP preconditioned resid norm 1.720960785852e-17 true resid norm
1.237111121391e-13 ||r(i)||/||b|| 1.275941911237e-15

  Linear solve converged due to CONVERGED_RTOL iterations 1

      Line search: Using full step: fnorm 9.695669610792e+01 gnorm
1.026572731653e-01

  1 SNES Function norm 1.026572731653e-01

    0 KSP Residual norm 1.382450412926e-04

    0 KSP preconditioned resid norm 1.382450412926e-04 true resid norm
1.026572731653e-01 ||r(i)||/||b|| 1.000000000000e+00

    1 KSP Residual norm 5.018078565710e-20

    1 KSP preconditioned resid norm 5.018078565710e-20 true resid norm
9.031463071676e-17 ||r(i)||/||b|| 8.797684560673e-16

  Linear solve converged due to CONVERGED_RTOL iterations 1

      Line search: Using full step: fnorm 1.026572731653e-01 gnorm
7.982937980399e-06

  2 SNES Function norm 7.982937980399e-06

    0 KSP Residual norm 4.223898196692e-08

    0 KSP preconditioned resid norm 4.223898196692e-08 true resid norm
7.982937980399e-06 ||r(i)||/||b|| 1.000000000000e+00

    1 KSP Residual norm 1.038123933240e-22

    1 KSP preconditioned resid norm 1.038123933240e-22 true resid norm
3.213931469966e-20 ||r(i)||/||b|| 4.026000800530e-15

  Linear solve converged due to CONVERGED_RTOL iterations 1

      Line search: Using full step: fnorm 7.982937980399e-06 gnorm
9.776066323463e-13

  3 SNES Function norm 9.776066323463e-13

Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 3

-n 2, final "iteration":

  0 SNES Function norm 9.695669610792e+01

    0 KSP Residual norm 7.898912593878e-03

    0 KSP preconditioned resid norm 7.898912593878e-03 true resid norm
9.695669610792e+01 ||r(i)||/||b|| 1.000000000000e+00

    1 KSP Residual norm 1.752819851736e-17

    1 KSP preconditioned resid norm 1.752819851736e-17 true resid norm
1.017605437996e-13 ||r(i)||/||b|| 1.049546322064e-15

  Linear solve converged due to CONVERGED_RTOL iterations 1

      Line search: Using full step: fnorm 9.695669610792e+01 gnorm
1.026572731655e-01

  1 SNES Function norm 1.026572731655e-01

    0 KSP Residual norm 1.382450412926e-04

    0 KSP preconditioned resid norm 1.382450412926e-04 true resid norm
1.026572731655e-01 ||r(i)||/||b|| 1.000000000000e+00

    1 KSP Residual norm 1.701690118486e-19

    1 KSP preconditioned resid norm 1.701690118486e-19 true resid norm
9.077679331860e-17 ||r(i)||/||b|| 8.842704517606e-16

  Linear solve converged due to CONVERGED_RTOL iterations 1

      Line search: Using full step: fnorm 1.026572731655e-01 gnorm
7.982937883350e-06

  2 SNES Function norm 7.982937883350e-06

    0 KSP Residual norm 4.223898196594e-08

    0 KSP preconditioned resid norm 4.223898196594e-08 true resid norm
7.982937883350e-06 ||r(i)||/||b|| 1.000000000000e+00

    1 KSP Residual norm 1.471638984554e-23

    1 KSP preconditioned resid norm 1.471638984554e-23 true resid norm
2.483672977401e-20 ||r(i)||/||b|| 3.111226735938e-15

  Linear solve converged due to CONVERGED_RTOL iterations 1

      Line search: Using full step: fnorm 7.982937883350e-06 gnorm
1.019121417798e-12

  3 SNES Function norm 1.019121417798e-12

Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 3

Of course these differences are still very small, but this is only true for
such a small problem size.  For a regular sized problem, the differences at
the final iteration can exceed 1 and even 100 at a particular grid point
(i.e. in a sense that doesn't scale with problem size).

I also compared -n 1 and -n 2 with the -snes_monitor_solution -ksp_view_rhs
-ksp_view_mat -ksp_view_solution options on a tiny problem (5x5x5), and I
was not able to find any differences in the Jacobian or the vectors, but
I'm suspicious that this could be due to the output format, because even
for the tiny problem there are non-trivial differences in the residuals of
both the SNES and the KSP.

In all cases, the differences in the residuals are localized to the
boundary between parts of the displacement vector owned by the two
processes.  The SNES residual with -n 2 typically looks discontinuous
across that boundary.

On Thu, Nov 9, 2017 at 11:16 AM, zakaryah . <zakaryah at gmail.com> wrote:

> Thanks Stefano, I will try what you suggest.
>
> Matt - my DM is a composite between the redundant field (loading
> coefficient, which is included in the Newton solve in Riks' method) and the
> displacements, which are represented by a 3D DA with 3 dof.  I am using
> finite difference.
>
> Probably my problem comes from confusion over how the composite DM is
> organized.  I am using FormFunction(), and within that I call
> DMCompositeGetLocalVectors(), DMCompositeScatter(), DMDAVecGetArray(), and
> for the Jacobian, DMCompositeGetLocalISs() and MatGetLocalSubmatrix() to
> split J into Jbb, Jbh, Jhb, and Jhh, where b is the loading coefficient,
> and h is the displacements).  The values of each submatrix are set using
> MatSetValuesLocal().
>
> I'm most suspicious of the part of the Jacobian routine where I calculate
> the rows of Jhb, the columns of Jbh, and the corresponding values.  I take
> the DA coordinates and ix,iy,iz, then calculate the row of Jhb as ((((iz-info->gzs)*info->gym
> + (iy-info->gys))*info->gxm + (ix-info->gxs))*info->dof+c), where info is
> the DA local info and c is the degree of freedom.  The same calculation is
> performed for the column of Jbh.  I suspect that the indexing of the DA
> vector is not so simple, but I don't know for a fact that I'm doing this
> incorrectly nor how to do this properly.
>
> Thanks for all the help!
>
>
> On Nov 9, 2017 8:44 AM, "Matthew Knepley" <knepley at gmail.com> wrote:
>
> On Thu, Nov 9, 2017 at 12:14 AM, zakaryah . <zakaryah at gmail.com> wrote:
>
>> Well the saga of my problem continues.  As I described previously in an
>> epic thread, I'm using the SNES to solve problems involving an elastic
>> material on a rectangular grid, subjected to external forces.  In any case,
>> I'm occasionally getting poor convergence using Newton's method with line
>> search.  In troubleshooting by visualizing the residual, I saw that in data
>> sets which had good convergence, the residual was nevertheless
>> significantly larger along the boundary between different processors.
>> Likewise, in data sets with poor convergence, the residual became very
>> large on the boundary between different processors.  The residual is not
>> significantly larger on the physical boundary, i.e. the global boundary.
>> When I run on a single process, convergence seems to be good on all data
>> sets.
>>
>> Any clues to fix this?
>>
>
> It sounds like something is wrong with communication across domains:
>
>  - If this is FEM, it sounds like you are not adding contributions from
> the other domain to shared vertices/edges/faces
>
>  - If this is FDM/FVM, maybe the ghosts are not updated
>
> What DM are you using? Are you using the Local assembly functions
> (FormFunctionLocal), or just FormFunction()?
>
>   Thanks,
>
>      Matt
>
> --
> 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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