gmres - restart and Gauss-Seidel

Fri Aug 15 08:15:34 CDT 2008

  0 KSP Residual norm 2.604671539574e+02
  1 KSP Residual norm 8.673339524769e+00
  2 KSP Residual norm 1.854343060681e+00
  3 KSP Residual norm 4.635172307027e-01
  4 KSP Residual norm 1.824358407207e-01
  5 KSP Residual norm 9.823366032782e-02
  6 KSP Residual norm 5.859833143089e-02
  7 KSP Residual norm 2.929617664041e-02
  8 KSP Residual norm 1.184403532587e-02
  9 KSP Residual norm 3.942287795560e-03
10 KSP Residual norm 4.611215310185e+00
                                             ^^^^^^^^^^^^^^^^^^^^^^

     This should never happen. This means there is an error
in your preconditioner, your smoother is not a linear operator
on its input variables. With GMRES, at restart the residual
norm should hardly change at all. The fact that it shoots
up means that the norm indicated in iteration 9 is totally wrong.

   If you run the gmres version with -ksp_monitor_true_residual
you will see that the true residual is not actually decreasing
like you think it is.

    Barry

On Aug 15, 2008, at 2:36 AM, Lukasz Kaczmarczyk wrote:

> Barry Smith wrote:
>>
>> On Aug 14, 2008, at 5:09 PM, Lukasz Kaczmarczyk wrote:
>>
>>> Hello,
>>> I have implementation of geometric multi-grid for heterogeneous
>>> quasi-brittle materials for hybrid-trefftz finite elements  
>>> (degrees of
>>> freedom are on faces -> small number of neighbours). Multi-grid
>>> algorithm need smoothing, for that I use Gauss-Seidel, however SOR
>>> implemented in PETSc is not parallel. That is way, I implemented  
>>> my own
>>> parallel Gauss-Seidel with colouring of faces in order to reduce
>>> communication. Everything seems to work prefect, except that that  
>>> for
>>> GMRES after restart algorithm is divergent.
>>                            ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>>
>>    What do you mean? It is converging fine until you hit the restart
>> iteration and
>> then get a totally different residual norm? And then each iteration  
>> gives
>> worse residuals?
>
> Thanks You all for response. No, algorithm is stable to next restart
>
>>
>>   Please run with -ksp_monitor_true_residual and send the output.
>> If the preconditioner is not actually a linear operator (i.e. it  
>> has a
>> bug in
>> smoother) then the residual norm computed  in GMRES may be wrong
>> and so GMRES may look like it is working but actually is basically
>> chugging on garbage. Also run with -ksp_type fgmres
>> -ksp_monitor_true_residual
>> and send the output.
>>
>
> I hope that this helps, I send three outputs:
> 1) -ksp_type gmres -ksp_gmres_restart 10
> 2) -ksp_type fgmres -ksp_gmres_restart 100 -ksp_monitor_true_residual
> 3) -ksp_type fgmres -ksp_gmres_restart 10  -ksp_monitor_true_residual
>
> 1) ksp_type gmres -ksp_gmres_restart 10
>
>  0 KSP Residual norm 2.604671539574e+02
>  1 KSP Residual norm 8.673339524769e+00
>  2 KSP Residual norm 1.854343060681e+00
>  3 KSP Residual norm 4.635172307027e-01
>  4 KSP Residual norm 1.824358407207e-01
>  5 KSP Residual norm 9.823366032782e-02
>  6 KSP Residual norm 5.859833143089e-02
>  7 KSP Residual norm 2.929617664041e-02
>  8 KSP Residual norm 1.184403532587e-02
>  9 KSP Residual norm 3.942287795560e-03
> 10 KSP Residual norm 4.611215310185e+00
> 11 KSP Residual norm 3.557713305907e-01
> 12 KSP Residual norm 1.911999331832e-01
> 13 KSP Residual norm 1.048287519555e-01
> 14 KSP Residual norm 5.745962963315e-02
> 15 KSP Residual norm 5.238562834476e-02
> 16 KSP Residual norm 5.046872351948e-02
> 17 KSP Residual norm 5.041805668527e-02
> 18 KSP Residual norm 4.952005417494e-02
> 19 KSP Residual norm 4.950805199415e-02
> 20 KSP Residual norm 8.581369434072e+00
> 21 KSP Residual norm 8.168490133118e-01
> 22 KSP Residual norm 1.416002910406e-01
> 23 KSP Residual norm 6.679961898612e-02
> 24 KSP Residual norm 5.031183883430e-02
> 25 KSP Residual norm 4.670843908572e-02
> 26 KSP Residual norm 4.662064456590e-02
> 27 KSP Residual norm 4.652217965668e-02
> 28 KSP Residual norm 4.611529866498e-02
> 29 KSP Residual norm 4.610330586416e-02
> 30 KSP Residual norm 9.139117000729e+00
> 31 KSP Residual norm 1.170939505327e+00
> 32 KSP Residual norm 1.783857007759e-01
> 33 KSP Residual norm 1.413658128682e-01
> 34 KSP Residual norm 1.411820201886e-01
> 35 KSP Residual norm 1.372634877051e-01
>
>
> 2) -ksp_type fgmres -ksp_gmres_restart 100 -ksp_monitor_true_residual
>  0 KSP Residual norm 8.770931682456e+05
>  0 KSP preconditioned resid norm 8.770931682456e+05 true resid norm
> 8.770931682456e+05 ||Ae||/||Ax|| 2.025559907164e+06
>  1 KSP Residual norm 1.466659768959e+00
>  1 KSP preconditioned resid norm 1.466659768959e+00 true resid norm
> 1.466659768959e+00 ||Ae||/||Ax|| 3.387105649673e+00
>  2 KSP Residual norm 2.135783619677e-01
>  2 KSP preconditioned resid norm 2.135783619677e-01 true resid norm
> 2.135783619678e-01 ||Ae||/||Ax|| 4.932380991006e-01
>  3 KSP Residual norm 1.342354228152e-01
>  3 KSP preconditioned resid norm 1.342354228152e-01 true resid norm
> 1.342354228151e-01 ||Ae||/||Ax|| 3.100034299884e-01
>  4 KSP Residual norm 7.872906297489e-02
>  4 KSP preconditioned resid norm 7.872906297489e-02 true resid norm
> 7.872906297491e-02 ||Ae||/||Ax|| 1.818169828064e-01
>  5 KSP Residual norm 3.414496482864e-02
>  5 KSP preconditioned resid norm 3.414496482864e-02 true resid norm
> 3.414496482865e-02 ||Ae||/||Ax|| 7.885441854116e-02
>  6 KSP Residual norm 2.025183908090e-02
>  6 KSP preconditioned resid norm 2.025183908090e-02 true resid norm
> 2.025183908092e-02 ||Ae||/||Ax|| 4.676961897981e-02
>  7 KSP Residual norm 1.023707179274e-02
>  7 KSP preconditioned resid norm 1.023707179274e-02 true resid norm
> 1.023707179279e-02 ||Ae||/||Ax|| 2.364150462111e-02
>  8 KSP Residual norm 4.938281368004e-03
>  8 KSP preconditioned resid norm 4.938281368004e-03 true resid norm
> 4.938281368031e-03 ||Ae||/||Ax|| 1.140447230867e-02
>  9 KSP Residual norm 2.373276511281e-03
>  9 KSP preconditioned resid norm 2.373276511281e-03 true resid norm
> 2.373276511245e-03 ||Ae||/||Ax|| 5.480847330515e-03
> 10 KSP Residual norm 1.180493643594e-03
> 10 KSP preconditioned resid norm 1.180493643594e-03 true resid norm
> 1.180493643635e-03 ||Ae||/||Ax|| 2.726233291716e-03
> 11 KSP Residual norm 7.142592937639e-04
> 11 KSP preconditioned resid norm 7.142592937639e-04 true resid norm
> 7.142592936809e-04 ||Ae||/||Ax|| 1.649511181911e-03
> 12 KSP Residual norm 4.226036746778e-04
> 12 KSP preconditioned resid norm 4.226036746778e-04 true resid norm
> 4.226036746206e-04 ||Ae||/||Ax|| 9.759613812110e-04
> 13 KSP Residual norm 2.572539106719e-04
> 13 KSP preconditioned resid norm 2.572539106719e-04 true resid norm
> 2.572539106261e-04 ||Ae||/||Ax|| 5.941024582002e-04
> 14 KSP Residual norm 1.444791718863e-04
> 14 KSP preconditioned resid norm 1.444791718863e-04 true resid norm
> 1.444791718510e-04 ||Ae||/||Ax|| 3.336603550419e-04
> 15 KSP Residual norm 8.492790274639e-05
> 15 KSP preconditioned resid norm 8.492790274639e-05 true resid norm
> 8.492790267409e-05 ||Ae||/||Ax|| 1.961325898824e-04
> 16 KSP Residual norm 4.707269600494e-05
> 16 KSP preconditioned resid norm 4.707269600494e-05 true resid norm
> 4.707269601177e-05 ||Ae||/||Ax|| 1.087097348555e-04
> 17 KSP Residual norm 2.692621130650e-05
> 17 KSP preconditioned resid norm 2.692621130650e-05 true resid norm
> 2.692621130585e-05 ||Ae||/||Ax|| 6.218342138276e-05
> 18 KSP Residual norm 1.339283607815e-05
> 18 KSP preconditioned resid norm 1.339283607815e-05 true resid norm
> 1.339283617815e-05 ||Ae||/||Ax|| 3.092943029068e-05
> 19 KSP Residual norm 8.006569523728e-06
> 19 KSP preconditioned resid norm 8.006569523728e-06 true resid norm
> 8.006569546889e-06 ||Ae||/||Ax|| 1.849038033273e-05
> 20 KSP Residual norm 5.048620120372e-06
> 20 KSP preconditioned resid norm 5.048620120372e-06 true resid norm
> 5.048620165524e-06 ||Ae||/||Ax|| 1.165928884641e-05
> 21 KSP Residual norm 3.079047055409e-06
> 21 KSP preconditioned resid norm 3.079047055409e-06 true resid norm
> 3.079047092852e-06 ||Ae||/||Ax|| 7.110754671622e-06
> 22 KSP Residual norm 1.837917124370e-06
> 22 KSP preconditioned resid norm 1.837917124370e-06 true resid norm
> 1.837917088425e-06 ||Ae||/||Ax|| 4.244487703000e-06
> 23 KSP Residual norm 8.755715968227e-07
> 23 KSP preconditioned resid norm 8.755715968227e-07 true resid norm
> 8.755715746951e-07 ||Ae||/||Ax|| 2.022045937380e-06
> 24 KSP Residual norm 4.460215115186e-07
> 24 KSP preconditioned resid norm 4.460215115186e-07 true resid norm
> 4.460215473811e-07 ||Ae||/||Ax|| 1.030042641779e-06
> 25 KSP Residual norm 2.074601204717e-07
> 25 KSP preconditioned resid norm 2.074601204717e-07 true resid norm
> 2.074601610498e-07 ||Ae||/||Ax|| 4.791087193129e-07
> 26 KSP Residual norm 1.078594582430e-07
> 26 KSP preconditioned resid norm 1.078594582430e-07 true resid norm
> 1.078594313079e-07 ||Ae||/||Ax|| 2.490906868011e-07
> 27 KSP Residual norm 5.595789534852e-08
> 27 KSP preconditioned resid norm 5.595789534852e-08 true resid norm
> 5.595808793116e-08 ||Ae||/||Ax|| 1.292296685216e-07
> 28 KSP Residual norm 2.866350154035e-08
> 28 KSP preconditioned resid norm 2.866350154035e-08 true resid norm
> 2.866379598785e-08 ||Ae||/||Ax|| 6.619620131833e-08
> 29 KSP Residual norm 1.602353949308e-08
> 29 KSP preconditioned resid norm 1.602353949308e-08 true resid norm
> 1.602386060096e-08 ||Ae||/||Ax|| 3.700552092568e-08
> 30 KSP Residual norm 8.795011075741e-09
> 30 KSP preconditioned resid norm 8.795011075741e-09 true resid norm
> 8.795292666765e-09 ||Ae||/||Ax|| 2.031185835503e-08
> 31 KSP Residual norm 4.077129947799e-09
> 31 KSP preconditioned resid norm 4.077129947799e-09 true resid norm
> 4.079852425518e-09 ||Ae||/||Ax|| 9.422015584506e-09
> 32 KSP Residual norm 1.739123114987e-09
> 32 KSP preconditioned resid norm 1.739123114987e-09 true resid norm
> 1.743717145343e-09 ||Ae||/||Ax|| 4.026942253017e-09
> 33 KSP Residual norm 8.452345380894e-10
> 33 KSP preconditioned resid norm 8.452345380894e-10 true resid norm
> 8.816532993133e-10 ||Ae||/||Ax|| 2.036091078762e-09
> 34 KSP Residual norm 3.861058363559e-10
> 34 KSP preconditioned resid norm 3.861058363559e-10 true resid norm
> 3.853896597046e-10 ||Ae||/||Ax|| 8.900192950935e-10
> 35 KSP Residual norm 1.986142320978e-10
>
> 3) -ksp_type fgmres -ksp_gmres_restart 10  -ksp_monitor_true_residual
>  0 KSP Residual norm 8.770931682456e+05
>  0 KSP preconditioned resid norm 8.770931682456e+05 true resid norm
> 8.770931682456e+05 ||Ae||/||Ax|| 2.025559907164e+06
>  1 KSP Residual norm 1.466659768959e+00
>  1 KSP preconditioned resid norm 1.466659768959e+00 true resid norm
> 1.466659768959e+00 ||Ae||/||Ax|| 3.387105649673e+00
>  2 KSP Residual norm 2.135783619677e-01
>  2 KSP preconditioned resid norm 2.135783619677e-01 true resid norm
> 2.135783619678e-01 ||Ae||/||Ax|| 4.932380991006e-01
>  3 KSP Residual norm 1.342354228152e-01
>  3 KSP preconditioned resid norm 1.342354228152e-01 true resid norm
> 1.342354228151e-01 ||Ae||/||Ax|| 3.100034299884e-01
>  4 KSP Residual norm 7.872906297489e-02
>  4 KSP preconditioned resid norm 7.872906297489e-02 true resid norm
> 7.872906297491e-02 ||Ae||/||Ax|| 1.818169828064e-01
>  5 KSP Residual norm 3.414496482864e-02
>  5 KSP preconditioned resid norm 3.414496482864e-02 true resid norm
> 3.414496482865e-02 ||Ae||/||Ax|| 7.885441854116e-02
>  6 KSP Residual norm 2.025183908090e-02
>  6 KSP preconditioned resid norm 2.025183908090e-02 true resid norm
> 2.025183908092e-02 ||Ae||/||Ax|| 4.676961897981e-02
>  7 KSP Residual norm 1.023707179274e-02
>  7 KSP preconditioned resid norm 1.023707179274e-02 true resid norm
> 1.023707179279e-02 ||Ae||/||Ax|| 2.364150462111e-02
>  8 KSP Residual norm 4.938281368004e-03
>  8 KSP preconditioned resid norm 4.938281368004e-03 true resid norm
> 4.938281368031e-03 ||Ae||/||Ax|| 1.140447230867e-02
>  9 KSP Residual norm 2.373276511281e-03
>  9 KSP preconditioned resid norm 2.373276511281e-03 true resid norm
> 2.373276511245e-03 ||Ae||/||Ax|| 5.480847330515e-03
> 10 KSP Residual norm 1.180493643635e-03
> 10 KSP preconditioned resid norm 1.180493643635e-03 true resid norm
> 1.180493643635e-03 ||Ae||/||Ax|| 2.726233291716e-03
> 11 KSP Residual norm 8.973593571160e-04
> 11 KSP preconditioned resid norm 8.973593571160e-04 true resid norm
> 8.973593570913e-04 ||Ae||/||Ax|| 2.072362665506e-03
> 12 KSP Residual norm 8.954054180580e-04
> 12 KSP preconditioned resid norm 8.954054180580e-04 true resid norm
> 8.954054180762e-04 ||Ae||/||Ax|| 2.067850236641e-03
> 13 KSP Residual norm 8.509609619524e-04
> 13 KSP preconditioned resid norm 8.509609619524e-04 true resid norm
> 8.509609619593e-04 ||Ae||/||Ax|| 1.965210161828e-03
> 14 KSP Residual norm 8.458566359370e-04
> 14 KSP preconditioned resid norm 8.458566359370e-04 true resid norm
> 8.458566359291e-04 ||Ae||/||Ax|| 1.953422225798e-03
> 15 KSP Residual norm 8.372984660266e-04
> 15 KSP preconditioned resid norm 8.372984660266e-04 true resid norm
> 8.372984660471e-04 ||Ae||/||Ax|| 1.933657979058e-03
> 16 KSP Residual norm 7.279198160941e-04
> 16 KSP preconditioned resid norm 7.279198160941e-04 true resid norm
> 7.279198160961e-04 ||Ae||/||Ax|| 1.681058807086e-03
> 17 KSP Residual norm 7.254072398644e-04
> 17 KSP preconditioned resid norm 7.254072398644e-04 true resid norm
> 7.254072398528e-04 ||Ae||/||Ax|| 1.675256260804e-03
> 18 KSP Residual norm 6.813582761007e-04
> 18 KSP preconditioned resid norm 6.813582761007e-04 true resid norm
> 6.813582760932e-04 ||Ae||/||Ax|| 1.573529536468e-03
> 19 KSP Residual norm 5.556242867367e-04
> 19 KSP preconditioned resid norm 5.556242867367e-04 true resid norm
> 5.556242867546e-04 ||Ae||/||Ax|| 1.283159326104e-03
> 20 KSP Residual norm 4.379413135337e-04
> 20 KSP preconditioned resid norm 4.379413135337e-04 true resid norm
> 4.379413135337e-04 ||Ae||/||Ax|| 1.011382141032e-03
> 21 KSP Residual norm 4.159789873039e-04
> 21 KSP preconditioned resid norm 4.159789873039e-04 true resid norm
> 4.159789873292e-04 ||Ae||/||Ax|| 9.606623212470e-04
> 22 KSP Residual norm 3.988218089618e-04
> 22 KSP preconditioned resid norm 3.988218089618e-04 true resid norm
> 3.988218089773e-04 ||Ae||/||Ax|| 9.210395150869e-04
> 23 KSP Residual norm 3.981102611370e-04
> 23 KSP preconditioned resid norm 3.981102611370e-04 true resid norm
> 3.981102611544e-04 ||Ae||/||Ax|| 9.193962657785e-04
> 24 KSP Residual norm 3.619785012910e-04
> 24 KSP preconditioned resid norm 3.619785012910e-04 true resid norm
> 3.619785013142e-04 ||Ae||/||Ax|| 8.359535406984e-04
> 25 KSP Residual norm 3.351791646576e-04
> 25 KSP preconditioned resid norm 3.351791646576e-04 true resid norm
> 3.351791646837e-04 ||Ae||/||Ax|| 7.740631238275e-04
> 26 KSP Residual norm 3.051027323014e-04
> 26 KSP preconditioned resid norm 3.051027323014e-04 true resid norm
> 3.051027323283e-04 ||Ae||/||Ax|| 7.046045785610e-04
> 27 KSP Residual norm 2.977852161346e-04
> 27 KSP preconditioned resid norm 2.977852161346e-04 true resid norm
> 2.977852161482e-04 ||Ae||/||Ax|| 6.877054988155e-04
> 28 KSP Residual norm 2.507200839706e-04
> 28 KSP preconditioned resid norm 2.507200839706e-04 true resid norm
> 2.507200839354e-04 ||Ae||/||Ax|| 5.790132318055e-04
> 29 KSP Residual norm 1.792952379074e-04
> 29 KSP preconditioned resid norm 1.792952379074e-04 true resid norm
> 1.792952379357e-04 ||Ae||/||Ax|| 4.140646155464e-04
> 30 KSP Residual norm 1.539920471163e-04
> 30 KSP preconditioned resid norm 1.539920471163e-04 true resid norm
> 1.539920471163e-04 ||Ae||/||Ax|| 3.556293994227e-04
> 31 KSP Residual norm 1.538529289011e-04
> 31 KSP preconditioned resid norm 1.538529289011e-04 true resid norm
> 1.538529288671e-04 ||Ae||/||Ax|| 3.553081195881e-04
> 32 KSP Residual norm 1.504592268331e-04
> 32 KSP preconditioned resid norm 1.504592268331e-04 true resid norm
> 1.504592268204e-04 ||Ae||/||Ax|| 3.474707004273e-04
> 33 KSP Residual norm 1.504404986449e-04
> 33 KSP preconditioned resid norm 1.504404986449e-04 true resid norm
> 1.504404986576e-04 ||Ae||/||Ax|| 3.474274495880e-04
> 34 KSP Residual norm 1.411298358801e-04
> 34 KSP preconditioned resid norm 1.411298358801e-04 true resid norm
> 1.411298358680e-04 ||Ae||/||Ax|| 3.259253949163e-04
> 35 KSP Residual norm 1.128668990420e-04
>
>
>