Something weird with SNES convergence reason

[Barry Smith]

DIVERGED_LS_FAILURE means that the direction computed by solving -  
J(u^n)^{-1} F(u^n) is NOT a descent direction
that is F(u^n - lambda * J(u^n)^{-1} F(u^n)) is not smaller than  
F(u^n) for 0 < lambda < 1.  Since you are solving the
linear system (in your last test) very accurately this almost always  
indicates the Jacobian is wrong. Please run with
-snes_type test and see what it says. Also recheck your Jacobian code.  
If this does not help then take a look at
src/snes/examples/tuturials/ex5.c and see how it can be run with  
fd_jacobian; you can try that with you code to
track down any errors in the Jacobian.

   Barry



On May 15, 2008, at 9:21 PM, Rafael Santos Coelho wrote:

> 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...
>