[Getdp] Re: getdp: conductivity, el. quasistatical approx.

Christophe Geuzaine Christophe.Geuzaine at ulg.ac.be
Wed Aug 1 14:51:21 CEST 2001

```Samuel Kvasnica wrote:
>
> > You cannot combine the electrostatic model and the electrokinetic model
> > the way you did: there are two different kinds of hypotheses involved
> > (predominant displacement or conduction currents) and you miss a time
> > derivative in the first term. For electrokinetics, you should solve
> >
> >      Equation {
> >       Galerkin { [ sigma[] * Dof{d v} , {d v} ] ;
> >                   In DomainC_Ele ;
> >      }
> >
>
> ok, but if I want to consider electrostatical effects between 2 DC circuits with high voltages should I then
> compute
> the electrokinetics first and then use computed potentials as boundary condition for electrostatics ? Can I do
> these
> 2 steps automatically in getdp ?

You can for example do it by using AssignFromResolution type
constraints, together with the DestinationSystem/TransferSolution
operations in the resolution. This way you could consider values from
one computation as strong essential boundary conditions in the second
problem (i.e. fix some Dofs in the second resolution with values
computed in the first). You could also couple the formulations through
weak boundary conditions (by simply referencing a quantity from one
formulation into the other and writing the appropriate surface term to
integrate). But I'm still not convinced that this coupling is the thing
to do in your case. I think you should first be sure of the hypotheses
you make, before attempting to solve anything...

>
> > If displacement and conduction currents are of the same order of
> > magnitude, you end up with the so-called electrodynamic model:
> >
> >      Equation {
> >        Galerkin { DtDof [ epsr[] * Dof{d v} , {d v} ] ;

Copy/paste mistake here: should be eps0*epsr[]!

> >                   In DomainCC_Ele ;
> >       Galerkin { [ sigma[] * Dof{d v} , {d v} ] ;
> >                   In DomainC_Ele ;
> >      }
> >
> > >
> > > How can I enhance this formulation further for harmonic quasistationary
> > >
> > > solution (without eddy currents) ? Do I have to solve it in time domain or
> > >
> > > it is possible to work just with complex amplitudes with equations like
> > >
> > > div eps*e = q, div((i*omega*eps+1/sigma)e+j_e) = 0
> >
> > Yes, simply define the above electrodynamic equations, and specify
> > 'Frequency omega/(2*Pi)' in the 'System' field of the resolution (cf.
> > http://www.geuz.org/getdp/doc/texinfo/getdp_7.html#SEC75). That's it:
> > the time derivative in the equations will be automatically transformed
> > into its appropriate harmonic representation.
>
> ok, that sounds good. I tried it, solve converges but at the and I get strange results displayed in gmsh -
> potential lines
> are dashed and it looks like there were missing mesh elements when I try to visualize them in option dialog of
> potential.

Don't forget to rerun the preprocessing before solving when you change
the type of the system you solve : the unknows are different (and twice
as many).

> I tried to display {v} and also Norm[{v}]. I looked into your magnetodynamics example to get some inspiration
> the ComplexValue option into my resolution, but that makes no effect. What's wrong (I'm sending you the files
> attached) ?

ComplexValue is implicitely assumed as soon as you give a frequency list
-> that's normal.

>
> > The concept hidden behind the definition of the Galerkin term is the one
> > of weak formulation. You can have a look on a rough example of how to
> > define a weak formulation from Maxwell's equations in the static case at
> > http://www.geuz.org/getdp/doc/slides/getdp-18.html. But you should
> > really consider reading any finite element introductory course. The book
> > from bossavit I mentioned above is definitely a good starting point. The
> > 'Integration' permits to specify the integration method to use.
>
> Yes, I borrowed it 2 days ago in my desperation but it looks like I'll need some weeks to swallow it. First
> I've got an impression
> of a book full of 'dry' theory written by a mathemacian, anyway after few pages I started to like it - just
> like the book of Birdsall
> on PIC methods.
>