[petsc-users] FEM on 2D poisson equation

[Matthew Knepley]

On Fri, Aug 2, 2013 at 10:30 PM, Olivier Bonnefon <
olivier.bonnefon at avignon.inra.fr> wrote:

> Hello,
>
> Just a mail to thank you for your help, I successfully simulate linear and
> non linear system (0=-\Delta u + u, and 0=-\Delta u - u(1-u)). The point
> was to know that "g0" is the derivative of f0 regarding u, in the PetscFEM
> struct.
>

Great! Thanks for your patience. Let us know if we can give any more help.

   Matt


> Olivier B.
>
>
> On 07/31/2013 05:43 PM, Jed Brown wrote:
>
>> Olivier Bonnefon<olivier.bonnefon@**avignon.inra.fr<olivier.bonnefon at avignon.inra.fr>>
>>  writes:
>>
>>  Hello,
>>>
>>> You are right. I have to define the Jacobian function of the variational
>>> formulation. I'm using snes and the petsFem struc (like in ex12).
>>>
>>> I need some information about the petscFem struct. I didn't find any
>>> document about that, is there one ?
>>>
>>> The field f0Funcs is used for the term \int f_0(u,gradu,x)*v
>>> The field f1Funcs is used for the term \int f_1(u,gradu,x).grad v
>>>
>>> Are f0 and f1 used for the rhs of the linearized problem ?
>>>
>> We think about these problems as being nonlinear whether they are or
>> not.  For a linear problem, you can apply one iteration of Newton's
>> method using '-snes_type ksponly'.  The Jacobian consists of the
>> derivatives of f_0 and f_1 with respect to u.
>>
>>  But what about g0,g1,g2 and g3 functions? I guess I have to use it to
>>> define the Jacobian ?
>>>
>> Those are the derivatives of the f_0 and f_1.
>>
>> For example, see the notation in Eq. 3 and 5 of this paper:
>>
>> http://59A2.org/na/Brown-**EfficientNonlinearSolversNodal**
>> HighOrder3D-2010.pdf<http://59A2.org/na/Brown-EfficientNonlinearSolversNodalHighOrder3D-2010.pdf>
>>
>
>
> --
> Olivier Bonnefon
> INRA PACA-Avignon, Unité BioSP
> Tel: +33 (0)4 32 72 21 58
>
>


-- 
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
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