On Dec 30, 2007, at 12:44 PM, Vijay M wrote:
Matt,
Thanks for the reply. What you suggested makes sense and so to start from a
common ground, I used no preconditioner at all in both the J-free and
analytical Jacobian cases. But now, interestingly, the analytical Jacobian
takes around twice the number of linear iterations.
mpirun -np 1 ex20 -ksp_type gmres -snes_monitor -pc_type none Number of Newton iterations = 6 Number of Linear iterations = 112 Average Linear its / Newton = 1.866667e+01
mpirun -np 1 ex20 -ksp_type gmres -snes_monitor -snes_mf -pc_type none Number of Newton iterations = 6 Number of Linear iterations = 54 Average Linear its / Newton = 9.000000e+00
I understand that both the methods will not give me the same number of total
linear iterations but a factor of 2 seems a little odd to me.
Yes, this is surprising.
Run with -ksp_monitor how are the linear convergence different?
This leads to
another question whether the user can actually change the epsilon used for
computing the perturbation in J-free scheme or is this fixed in PETSc ?
If not, then what do you think is the reason for this ?
Barry
Do let me know your comments when you get some time. Thanks.
Vijay
-----Original Message-----
From: owner-petsc-users@xxxxxxxxxxx [mailto:owner-petsc-users@xxxxxxxxxxx ]
On Behalf Of Matthew Knepley
Sent: Saturday, December 29, 2007 9:05 PM
To: petsc-users@xxxxxxxxxxx
Subject: Re: Matrix free example snes/ex20.c
On Dec 29, 2007 8:07 PM, Vijay M <vijay.m@xxxxxxxxx> wrote:residualHi all,
I was trying to compile and run the ex20.c example code in the tutorial
section of SNES. Although it does not explicitly specify that - snes_mf
option can be used, my understanding is that as long as a nonlinearfunction is written correctly, PETSc will calculate via finite difference
the action of the Jacobian on a given vector. Is that correct ?
Yes.
Now if that is the case, then please observe the discrepancy in the number
of linear iterations taken with an analytical Jacobian and matrix- free
option. What puzzles me is that the SNES function norm are quite close for
both the methods but the linear iterations differ by a factor of 3. Why
exactly is this ?
There is no PC when using -snes_mf whereas the default is ILU for the analytic Jacobian.
Matt
Here's the output to make this clearer.
vijay :mpirun -np 1 ex20 -ksp_type gmres -snes_monitor
0 SNES Function norm 2.271442542876e-01
1 SNES Function norm 6.881516100891e-02
2 SNES Function norm 1.813939751552e-02
3 SNES Function norm 2.354176462207e-03
4 SNES Function norm 3.063728077362e-05
5 SNES Function norm 3.106106268946e-08
6 SNES Function norm 5.344742712545e-12
0 SNES Function norm 2.271442542876e-01
1 SNES Function norm 6.881516100891e-02
2 SNES Function norm 1.813939751552e-02
3 SNES Function norm 2.354176462207e-03
4 SNES Function norm 3.063728077362e-05
5 SNES Function norm 3.106106268946e-08
6 SNES Function norm 5.344742712545e-12
Number of Newton iterations = 6
Number of Linear iterations = 18
Average Linear its / Newton = 3.000000e+00
vijay :mpirun -np 1 ex20 -ksp_type gmres -snes_monitor -snes_mf
0 SNES Function norm 2.271442542876e-01
1 SNES Function norm 6.870629867542e-02
2 SNES Function norm 1.804335379848e-02
3 SNES Function norm 2.290074339682e-03
4 SNES Function norm 3.082384186373e-05
5 SNES Function norm 3.926396277038e-09
6 SNES Function norm 3.754922566585e-16
0 SNES Function norm 2.271442542876e-01
1 SNES Function norm 6.870629867542e-02
2 SNES Function norm 1.804335379848e-02
3 SNES Function norm 2.290074339682e-03
4 SNES Function norm 3.082384186373e-05
5 SNES Function norm 3.926396277038e-09
6 SNES Function norm 3.754922566585e-16
Number of Newton iterations = 6
Number of Linear iterations = 54
Average Linear its / Newton = 9.000000e+00
Thanks,
Vijay
-- 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