[Getdp] [Fwd: a coupled problem]

[Christophe Geuzaine]

Hi,

You have to linearize the second equation. You may use

* a Picard scheme: just take e.g. rho at the previous iteration in your
second equation (i.e. write {rho} and not Dof{rho}) and solve the
problem iteratively in an IterativeLoop operation (cf. user's guide).

* a Newton-Raphson scheme: you have to give an expression for the
jacobian matrix in a JacNL equation term. Unfortunately, there are still
some elementary tools (i.e. finite difference computation of
derivatives) missing to write these terms easily.

Christophe

Christophe Geuzaine wrote:
> 
> jmwei wrote:
> >
> > Dear Christophe Geuzaine,
> >          I am a student at the University Duisburg. I have found getdp at the internet recently.  I think it is a very wonderful and useful
> > software. During my current work, I have encountered a electrical field -- space charge coupled problem. Basically, this
> > problem can be described using the following two equations:
> >
> >                              div (epsilon*e)  + rho = 0                                  and
> >                              div (rho * ( -k*e + U) )   = 0
> >
> >  here epsilon , k (ion mobility) and U ( velocity field ) are all constant; while e is the electrical field and rho the space charge density.
> >  I wonder if Getdp can be used to solve such a coupled problem. If it can, how can I define the formulation? In the 2nd equation
> > , there is a term including the product of two unknowns, i.e.  rho*e. But getdp only allows one dof in a Galerkin definition.
> >
> >
> >          Express my great thanks in advance!
> >          Best regards !
> >
> >            Wei
> >             wei at uni-duisburg.de
> 
> --
> Christophe Geuzaine
> 
> Tel: 32 (0) 4 366 37 10    http://geuz.org
> Fax: 32 (0) 4 366 29 10    mailto:Christophe.Geuzaine at ulg.ac.be
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-- 
Christophe Geuzaine

Tel: 32 (0) 4 366 37 10    http://geuz.org
Fax: 32 (0) 4 366 29 10    mailto:Christophe.Geuzaine at ulg.ac.be