[petsc-users] compare snes_mf_operator and snes_fd

Jed Brown jedbrown at mcs.anl.gov
Thu Jan 31 13:46:57 CST 2013 

On Thu, Jan 31, 2013 at 1:29 PM, Matthew Knepley <knepley at gmail.com> wrote:

> On Thu, Jan 31, 2013 at 2:25 PM, Zou (Non-US), Ling <ling.zou at inl.gov>wrote:
>
>>
>>
>> On Thu, Jan 31, 2013 at 11:28 AM, Matthew Knepley <knepley at gmail.com>wrote:
>>
>>> On Thu, Jan 31, 2013 at 1:16 PM, Zou (Non-US), Ling <ling.zou at inl.gov>wrote:
>>>
>>>> Thank you Matt and Barry. I didn't get a chance to reply you yesterday.
>>>> Here are the new output files with -snes_view on.
>>>>
>>>
>>> It seems clear that the matrix you are providing to snes_mf_operator is
>>> not a good
>>> preconditioner for the actual matrix obtained with snes_fd. Maybe you
>>> have a bug in
>>> your evaluation. Maybe you could try -snes_check_jacobian to see.
>>>
>>>     Matt
>>>
>>
>> Thank you Matt. -snes_check_jacobian options seems not working (I am
>> using PETSc 3.3p4).
>>
>
That option is in petsc-dev, use -snes_type test or -snes_compare_explicit
in petsc-3.3. If you are using MOOSE, then chances are you have not
assembled an exact Jacobian thus these will show a difference even if
everything is "working fine". Checking convergence with -snes_mf_operator
-pc_type lu as you have done is a good test for whether an inexact Jacobian
is still a good approximation. You might have to assembly an off-diagonal
block, for example.


> However, now I got a clue what I need to improve. By the way, as ksp needs
>> the Pmat as the matrix for preconditioning procedure, is there any way let
>> ksp use the finite difference matrix provided by snes? or this is exactly
>> what snes_fd is doing.
>>
>
> That is what snes_fd is doing.
>
>
>> Also, could you explain a bit more about the wired 'true resid norm'
>> drops and increases behavior?
>>
>>     0 KSP unpreconditioned resid norm 7.527570931028e-02 true resid norm
>> 7.527570931028e-02 ||r(i)||/||b|| 1.000000000000e+00
>>     1 KSP unpreconditioned resid norm 7.217693018525e-06 true resid norm
>> 7.217693018525e-06 ||r(i)||/||b|| 9.588342753138e-05
>>     2 KSP unpreconditioned resid norm 1.052214184181e-07 true resid norm
>> 1.410618177438e-02 ||r(i)||/||b|| 1.873935417365e-01
>>     3 KSP unpreconditioned resid norm 1.023527631618e-07 true resid norm
>> 1.410612986979e-02 ||r(i)||/||b|| 1.873928522101e-01
>>     4 KSP unpreconditioned resid norm 1.930893544395e-08 true resid norm
>> 1.408238386773e-02 ||r(i)||/||b|| 1.870773984964e-01
>>
>
> This looks like you are losing orthogonality in the GMRES basis after step
> 1. Maybe try *-ksp_gmres_modifiedgramschmidt*
> You have an error in your Jacobian.
>

I would also be concerned about finite differencing error. Does the
convergence behavior change at all if you use -mat_mffd_type ds?


> *   *Matt
>
>
>> Ling
>>
>>
>>
>>>
>>>> Ling
>>>>
>>>>
>>>> On Wed, Jan 30, 2013 at 6:40 PM, Matthew Knepley <knepley at gmail.com>wrote:
>>>>
>>>>> On Wed, Jan 30, 2013 at 6:30 PM, Zou (Non-US), Ling <ling.zou at inl.gov>wrote:
>>>>>
>>>>>> Hi, All
>>>>>>
>>>>>> I am testing the performance of snes_mf_operator against snes_fd.
>>>>>>
>>>>>
>>>>> You need to give -snes_view so we can see what solver is begin used.
>>>>>
>>>>>   Matt
>>>>>
>>>>>> I know snes_fd is for test/debugging and extremely slow, which is ok
>>>>>> for my testing purpose. I then compared the code performance using
>>>>>> snes_mf_operator against snes_fd. Of course, snes_mf_operator uses way less
>>>>>> computing time then snes_fd, however, the snes_mf_operator non-linear
>>>>>> solver performance is worse than snes_fd, in terms of non linear iteration
>>>>>> in each time steps.
>>>>>>
>>>>>> Here is the PETSc Options Table entries taken from the log_summary
>>>>>> when using snes_mf_operator
>>>>>> #PETSc Option Table entries:
>>>>>> -ksp_converged_reason
>>>>>> -ksp_gmres_restart 300
>>>>>> -ksp_monitor_true_residual
>>>>>> -log_summary
>>>>>> -m pipe_7eqn_2phase_step7_ps.i
>>>>>> -mat_fd_type ds
>>>>>> -pc_type lu
>>>>>> -snes_mf_operator
>>>>>> -snes_monitor
>>>>>> #End of PETSc Option Table entries
>>>>>>
>>>>>> Here is the PETSc Options Table entries taken from the log_summary
>>>>>> when using snes_fd
>>>>>> #PETSc Option Table entries:
>>>>>> -ksp_converged_reason
>>>>>> -ksp_gmres_restart 300
>>>>>> -ksp_monitor_true_residual
>>>>>> -log_summary
>>>>>> -m pipe_7eqn_2phase_step7_ps.i
>>>>>> -mat_fd_type ds
>>>>>> -pc_type lu
>>>>>> -snes_fd
>>>>>> -snes_monitor
>>>>>> #End of PETSc Option Table entries
>>>>>>
>>>>>> The full code output along with log_summary are attached.
>>>>>>
>>>>>> I've noticed that when using snes_fd, the non-linear convergence is
>>>>>> always good in each time step, around 3-4 non-linear steps with almost
>>>>>> quadratic convergence rate. In each non-linear step, it uses only 1 linear
>>>>>> step to converge as I used '-pc_type lu' and only 1 linear step is
>>>>>> expected. Here is a piece of output I pulled out from the code output (very
>>>>>> nice non-linear, linear performance but of course very expensive):
>>>>>>
>>>>>> DT: 1.234568e-05
>>>>>>  Solving time step  7, time=4.34568e-05...
>>>>>>   Initial |residual|_2 = 3.547156e+00
>>>>>>   NL step  0, |residual|_2 = 3.547156e+00
>>>>>>   0 SNES Function norm 3.547155872103e+00
>>>>>>     0 KSP unpreconditioned resid norm 3.547155872103e+00 true resid
>>>>>> norm 3.547155872103e+00 ||r(i)||/||b|| 1.000000000000e+00
>>>>>>     1 KSP unpreconditioned resid norm 3.128472759493e-15 true resid
>>>>>> norm 2.343197746412e-15 ||r(i)||/||b|| 6.605849392864e-16
>>>>>>   Linear solve converged due to CONVERGED_RTOL iterations 1
>>>>>>   NL step  1, |residual|_2 = 4.900005e-04
>>>>>>   1 SNES Function norm 4.900004596844e-04
>>>>>>     0 KSP unpreconditioned resid norm 4.900004596844e-04 true resid
>>>>>> norm 4.900004596844e-04 ||r(i)||/||b|| 1.000000000000e+00
>>>>>>     1 KSP unpreconditioned resid norm 5.026229113909e-18 true resid
>>>>>> norm 1.400595243895e-17 ||r(i)||/||b|| 2.858354959089e-14
>>>>>>   Linear solve converged due to CONVERGED_RTOL iterations 1
>>>>>>   NL step  2, |residual|_2 = 1.171419e-06
>>>>>>   2 SNES Function norm 1.171419468770e-06
>>>>>>     0 KSP unpreconditioned resid norm 1.171419468770e-06 true resid
>>>>>> norm 1.171419468770e-06 ||r(i)||/||b|| 1.000000000000e+00
>>>>>>     1 KSP unpreconditioned resid norm 5.679448617332e-21 true resid
>>>>>> norm 4.763172202015e-21 ||r(i)||/||b|| 4.066154207782e-15
>>>>>>   Linear solve converged due to CONVERGED_RTOL iterations 1
>>>>>>   NL step  3, |residual|_2 = 1.860041e-08
>>>>>>   3 SNES Function norm 1.860041398803e-08
>>>>>> Converged:1
>>>>>>
>>>>>> Back to the snes_mf_operator option, it behaviors differently. It
>>>>>> generally takes more non-linear and linear steps. The 'KSP unpreconditioned
>>>>>> resid norm' drops nicely however the 'true resid norm' seems to be a bit
>>>>>> wired to me, drops then increases.
>>>>>>
>>>>>> DT: 1.524158e-05
>>>>>>  Solving time step  9, time=7.24158e-05...
>>>>>>   Initial |residual|_2 = 3.601003e+00
>>>>>>   NL step  0, |residual|_2 = 3.601003e+00
>>>>>>   0 SNES Function norm 3.601003423006e+00
>>>>>>     0 KSP unpreconditioned resid norm 3.601003423006e+00 true resid
>>>>>> norm 3.601003423006e+00 ||r(i)||/||b|| 1.000000000000e+00
>>>>>>     1 KSP unpreconditioned resid norm 5.931429724028e-02 true resid
>>>>>> norm 5.931429724028e-02 ||r(i)||/||b|| 1.647160257092e-02
>>>>>>     2 KSP unpreconditioned resid norm 1.379343811770e-05 true resid
>>>>>> norm 5.203950797327e+00 ||r(i)||/||b|| 1.445139086534e+00
>>>>>>     3 KSP unpreconditioned resid norm 4.432805478482e-08 true resid
>>>>>> norm 5.203984109211e+00 ||r(i)||/||b|| 1.445148337256e+00
>>>>>>   Linear solve converged due to CONVERGED_RTOL iterations 3
>>>>>>   NL step  1, |residual|_2 = 5.928815e-02
>>>>>>   1 SNES Function norm 5.928815267199e-02
>>>>>>     0 KSP unpreconditioned resid norm 5.928815267199e-02 true resid
>>>>>> norm 5.928815267199e-02 ||r(i)||/||b|| 1.000000000000e+00
>>>>>>     1 KSP unpreconditioned resid norm 3.276993782949e-06 true resid
>>>>>> norm 3.276993782949e-06 ||r(i)||/||b|| 5.527232061148e-05
>>>>>>     2 KSP unpreconditioned resid norm 2.082083269186e-08 true resid
>>>>>> norm 1.551766076370e-05 ||r(i)||/||b|| 2.617329106129e-04
>>>>>>   Linear solve converged due to CONVERGED_RTOL iterations 2
>>>>>>   NL step  2, |residual|_2 = 3.340603e-05
>>>>>>   2 SNES Function norm 3.340603450829e-05
>>>>>>     0 KSP unpreconditioned resid norm 3.340603450829e-05 true resid
>>>>>> norm 3.340603450829e-05 ||r(i)||/||b|| 1.000000000000e+00
>>>>>>     1 KSP unpreconditioned resid norm 6.659426858789e-07 true resid
>>>>>> norm 6.659426858789e-07 ||r(i)||/||b|| 1.993480207037e-02
>>>>>>     2 KSP unpreconditioned resid norm 6.115119674466e-07 true resid
>>>>>> norm 2.887921320245e-06 ||r(i)||/||b|| 8.644909109246e-02
>>>>>>     3 KSP unpreconditioned resid norm 1.907116539439e-09 true resid
>>>>>> norm 1.000874623281e-06 ||r(i)||/||b|| 2.996089293486e-02
>>>>>>     4 KSP unpreconditioned resid norm 3.383211446515e-12 true resid
>>>>>> norm 1.005586686459e-06 ||r(i)||/||b|| 3.010194718591e-02
>>>>>>   Linear solve converged due to CONVERGED_RTOL iterations 4
>>>>>>   NL step  3, |residual|_2 = 2.126180e-05
>>>>>>   3 SNES Function norm 2.126179867301e-05
>>>>>>     0 KSP unpreconditioned resid norm 2.126179867301e-05 true resid
>>>>>> norm 2.126179867301e-05 ||r(i)||/||b|| 1.000000000000e+00
>>>>>>     1 KSP unpreconditioned resid norm 2.724944027954e-06 true resid
>>>>>> norm 2.724944027954e-06 ||r(i)||/||b|| 1.281615008147e-01
>>>>>>     2 KSP unpreconditioned resid norm 7.933800605616e-10 true resid
>>>>>> norm 2.776823963042e-06 ||r(i)||/||b|| 1.306015547295e-01
>>>>>>     3 KSP unpreconditioned resid norm 6.130449965920e-11 true resid
>>>>>> norm 2.777694372634e-06 ||r(i)||/||b|| 1.306424924510e-01
>>>>>>     4 KSP unpreconditioned resid norm 2.090637685604e-13 true resid
>>>>>> norm 2.777696567814e-06 ||r(i)||/||b|| 1.306425956963e-01
>>>>>>   Linear solve converged due to CONVERGED_RTOL iterations 4
>>>>>>   NL step  4, |residual|_2 = 2.863517e-06
>>>>>>   4 SNES Function norm 2.863517221239e-06
>>>>>>     0 KSP unpreconditioned resid norm 2.863517221239e-06 true resid
>>>>>> norm 2.863517221239e-06 ||r(i)||/||b|| 1.000000000000e+00
>>>>>>     1 KSP unpreconditioned resid norm 2.518692933040e-10 true resid
>>>>>> norm 2.518692933039e-10 ||r(i)||/||b|| 8.795801590987e-05
>>>>>>     2 KSP unpreconditioned resid norm 2.165272180327e-12 true resid
>>>>>> norm 1.136392813468e-09 ||r(i)||/||b|| 3.968520967987e-04
>>>>>>   Linear solve converged due to CONVERGED_RTOL iterations 2
>>>>>>   NL step  5, |residual|_2 = 9.132390e-08
>>>>>>   5 SNES Function norm 9.132390063388e-08
>>>>>> Converged:1
>>>>>>
>>>>>>
>>>>>> My questions:
>>>>>> 1, Is it true? when using snes_fd, the real Jacobian matrix, say J,
>>>>>> is explicitly constructed. when combined with -pc_type lu, the problem
>>>>>> J (du) = -R
>>>>>> is directly solved as (du) = J^{-1} * (-R)
>>>>>> where J^{-1} is calculated from this explicitly constructed matrix J,
>>>>>> using LU factorization.
>>>>>>
>>>>>> 2, what's the difference between snes_mf_operator and snes_fd?
>>>>>> What I understand (might be wrong) is snes_mf_operator does not
>>>>>> *explicitly construct* the matrix J, as it is a matrix free method. Is the
>>>>>> finite differencing methods behind the matrix free operator
>>>>>> in snes_mf_operator and the matrix construction in snes_fd are the same?
>>>>>>
>>>>>> 3, It seems that snes_mf_operator is preconditioned, while snes_fd is
>>>>>> not. Why it says ' KSP unpreconditioned resid norm ' but I am expecting
>>>>>> 'KSP preconditioned resid norm'. Also if it is 'unpreconditioned',
>>>>>> should it be identical to the 'true resid norm'? Is it my fault, for
>>>>>> example, giving a bad preconditioning matrix, makes the KSP not working
>>>>>> well?
>>>>>>
>>>>>> I'd appreciate your help...there are too many (maybe bad) questions
>>>>>> today. And please let me know if you may need more information.
>>>>>>
>>>>>> Best,
>>>>>>
>>>>>> Ling
>>>>>>
>>>>>
>>>>>
>>>>>
>>>>> --
>>>>> 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
>>>>>
>>>>
>>>>
>>>
>>>
>>> --
>>> 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
>>>
>>
>>
>
>
> --
> 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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