[petsc-users] FEM on 2D poisson equation

[Olivier Bonnefon]

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.

Olivier B.

On 07/31/2013 05:43 PM, Jed Brown wrote:
> Olivier Bonnefon<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-EfficientNonlinearSolversNodalHighOrder3D-2010.pdf


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