[petsc-users] compare snes_mf_operator and snes_fd
Zou (Non-US), Ling
ling.zou at inl.gov
Thu Jan 31 12:16:34 CST 2013
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.
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
>
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