[petsc-users] compare snes_mf_operator and snes_fd

Wed Jan 30 20:50:05 CST 2013

  Also see http://www.mcs.anl.gov/petsc/documentation/faq.html#newton

On Jan 30, 2013, at 7:40 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