[petsc-users] compare snes_mf_operator and snes_fd

Thu Jan 31 13:25:39 CST 2013

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.

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

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
>
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