[petsc-users] compare snes_mf_operator and snes_fd

Thu Jan 31 13:29:15 CST 2013

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). 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.
*   *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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