[petsc-users] compare snes_mf_operator and snes_fd
Zou (Non-US), Ling
ling.zou at inl.gov
Wed Jan 30 17:30:17 CST 2013
Hi, All
I am testing the performance of snes_mf_operator against snes_fd.
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
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