# Something weird with SNES convergence reason

Rafael Santos Coelho rafaelsantoscoelho at gmail.com
Thu May 15 21:21:56 CDT 2008

```Hi people,

thank you very much for the help. I couldn't fix the problem though...

Matthew:

1) I guess so because for the vast majority of the tests carried out, the
method converges and you can actually observe norm(F(x)) decreasing with few
Newton iterations. For example:

\$ mpirun -np 2 ./bratu_problem -N 16 -M 16 -P 16 -ksp_converged_reason
-snes_converged_reason -ksp_type lcd -pc_type jacobi -ksp_monitor

0 KSP Residual norm 5.960419091967e-01
1 KSP Residual norm 1.235318806330e+00
(...)
Linear solve converged due to CONVERGED_RTOL iterations 56
0 KSP Residual norm 2.990541631546e-02
1 KSP Residual norm 1.332572441021e-02
(...)
29 KSP Residual norm 3.225505605549e-07
30 KSP Residual norm 1.658059885118e-07
Linear solve converged due to CONVERGED_RTOL iterations 30
0 KSP Residual norm 7.629434752036e-05
1 KSP Residual norm 1.413056976255e-05
(...)
21 KSP Residual norm 1.183900079277e-09
22 KSP Residual norm 6.010910804534e-10

Linear solve converged due to CONVERGED_RTOL iterations 22
Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE

2) The governing PDE is  -Laplacian(u) + d * u_x -lambda * exp(u) = 0 and u
= 0 in all domain boundaries. u_x stands for the partial derivative of u
with respect to the x variable, where u = u(x, y, z). For all the tests I
made, d = 16 and lambda = 32. I tried setting d = 0, but the error
continued.

Barry:

Consider

\$ mpirun -np 8 ./bratu_problem -x 16 -y 16 -z 16 -ksp_converged_reason
-snes_converged_reason -ksp_type lcd -pc_type jacobi -ksp_monitor

Here's the output:

0 KSP Residual norm 5.960419091967e-01
1 KSP Residual norm 1.235318806330e+00
(...)
55 KSP Residual norm 7.533575286046e-06
56 KSP Residual norm 4.924747432423e-06
Linear solve converged due to CONVERGED_RTOL iterations 56
0 KSP Residual norm 5.899667305071e-01
1 KSP Residual norm 1.233037780509e+00
(...)
56 KSP Residual norm 9.299650766487e-06
57 KSP Residual norm 5.541388445894e-06
Linear solve converged due to CONVERGED_RTOL iterations 57
0 KSP Residual norm 5.898541843665e-01
1 KSP Residual norm 1.230515227262e+00
(...)
57 KSP Residual norm 6.065473514455e-06
58 KSP Residual norm 3.255910272791e-06

Linear solve converged due to CONVERGED_RTOL iterations 58
Nonlinear solve did not converge due to DIVERGED_LS_FAILURE

Now, if I use -ksp_rtol 1.e-10, same thing occurs, the only difference is
that the number of linear iterations per nonlinear iteration gets bigger (as
one might have expected).

I'm using the classic 7-point stencil finite difference approximation to
discretize the PDE...
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