[petsc-users] petsc-3.5.2: ex12 with Neumann BC

[Olivier Bonnefon]

Hello,

Thank you for your answer, I agree with you.

I have adapted the ex12 example for the system:

-\nabla \nabla u + u + f = 0 in \Omega  (1)

with f = 4-x^2-y^2
The solution is still x^2-y^2.

It consists in adding the following gradient function:

void g0_uu(const PetscScalar u[], const PetscScalar u_t[], const 
PetscScalar u_x[], const PetscScalar a[], const PetscScalar a_t[], const 
PetscScalar a_x[], const PetscReal x[], PetscScalar g0[])
{
   g0[0] = 1.0;
}
...
//and set gradient
ierr = PetscDSSetJacobian(prob, 0, 0, g0_uu, NULL, NULL, 
g3_uu);CHKERRQ(ierr);
...
Of course, I have modified the f0_u function.


With Dirichlet BC, I get the solution.

With Neumann BC, the solution is still shifted down (-2/3). The problem 
(1) with Neumann BC has a unique solution.
How remove the condition \int_\Omega u = 0 ?

Thanks
Olivier Bonnefon





On 11/06/2014 07:14 AM, Matthew Knepley wrote:
> On Mon, Nov 3, 2014 at 9:46 AM, Olivier Bonnefon 
> <olivier.bonnefon at avignon.inra.fr 
> <mailto:olivier.bonnefon at avignon.inra.fr>> wrote:
>
>     Hello,
>
>     Thank for your answer, I'll explain my trouble:
>
>     My problem is that the BC Neumann leads to wrong result.
>
>     With Dirichlet BC, I get:
>     -------------------------------
>
>     > ./ex12 -run_type full -refinement_limit 0.0 -bc_type dirichlet
>     -interpolate 0 -petscspace_order 1 -show_initial -show_solution
>     -dm_plex_print_fem 1
>     ...
>     ...
>     Solution
>     Vec Object:potential 1 MPI processes
>       type: seq
>     0.5
>
>     This result is correct.
>
>     With Neuman BC, I get:
>     --------------------------------
>
>     > ./ex12 -run_type full -refinement_limit 0.0 -bc_type neumann
>     -interpolate 1 -petscspace_order 1 -show_initial
>     -dm_plex_print_fem 1 -show_solution -bd_petscspace_order 1
>     -snes_linesearch_monitor -snes_monitor -ksp_monitor_true_residual
>     -snes_converged_reason -ksp_converged_reason
>     ....
>     ....
>
>
>     Solution
>     Vec Object:potential 1 MPI processes
>       type: seq
>     -0.75
>     -0.583333
>     0.0833333
>     -0.583333
>     -0.333333
>     0.416667
>     0.0833333
>     0.416667
>     1.25
>
>
>     That is not the values of the solution x*x+y*y.
>
>
> Sorry, this is poor documentation on my part. I will fix it in the 
> example. The Naumann solution
> explicitly discards the constant part, meaning
>
>   \int_\Omega u = 0
>
> If we look at my solution
>
>   \int^1_0 dx \int^1_0 dy x^2 + y^2 = 2/3
>
> However, this is for the continuum result, whereas we are enforcing 
> this in the discrete case.
> Thus, what we really get is 0.75, since we are integrating linear 
> patches instead of quadratic
> patches. After shifting by that, you still do not get exactly x^2 + 
> y^2 since there is some
> discretization error. If you run with P2 you should get the exact 
> answer, shifted down to eliminate
> the DC component.
>
>   Thanks,
>
>      Matt
>
>
>     I tried many ksp options.
>     Moreover, the neumann BC with "-run_type full" is not cover in the
>     list
>     https://bitbucket.org/petsc/petsc/src/fced3c3f9e703542693913793d15321603e40fe6/config/builder.py?at=master#cl-257
>
>     Do you know what is wrong ?
>
>     Thanks,
>
>     Olivier Bonnefon
>
>     On 10/31/2014 06:50 PM, Matthew Knepley wrote:
>>     On Fri, Oct 31, 2014 at 10:43 AM, Olivier Bonnefon
>>     <olivier.bonnefon at avignon.inra.fr
>>     <mailto:olivier.bonnefon at avignon.inra.fr>> wrote:
>>
>>         Hello,
>>
>>         I'm working on the snes/examples/tutorial/ex12 version 3.5.2.
>>
>>         I didn't succed to run the simplest case with Neumann BC:
>>
>>         ./ex12 -run_type full -refinement_limit 0.0 -bc_type neumann
>>         -interpolate 1 -petscspace_order 1 -show_initial
>>         -dm_plex_print_fem 1 -show_solution -bd_petscspace_order 1
>>         -snes_linesearch_monitor -snes_monitor
>>         -ksp_monitor_true_residual -snes_converged_reason
>>         -ksp_converged_reason
>>
>>         This leads to dofs negatives values.
>>
>>
>>     I do not understand what you mean. Please always mail the full
>>     error message.
>>
>>         Do you know the options to get a correct result with Neumann BC ?
>>
>>
>>     There are some tests here:
>>
>>     https://bitbucket.org/petsc/petsc/src/fced3c3f9e703542693913793d15321603e40fe6/config/builder.py?at=master#cl-257
>>
>>        Matt
>>
>>         Regards,
>>         Olivier Bonnefon
>>
>>
>>
>>
>>     -- 
>>     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
>
>
>     -- 
>     Olivier Bonnefon
>     INRA PACA-Avignon, Unité BioSP
>     Tel:+33 (0)4 32 72 21 58  <tel:%2B33%20%280%294%2032%2072%2021%2058>
>
>
>
>
> -- 
> 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


-- 
Olivier Bonnefon
INRA PACA-Avignon, Unité BioSP
Tel: +33 (0)4 32 72 21 58

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