[Getdp] [GetDP] Calculation of an Integral quantity
Christophe Geuzaine
cgeuzaine at ulg.ac.be
Tue Apr 24 15:17:05 CEST 2007
Olivier Castany wrote:
> Hello,
>
> I would like to compute a magnetic field in two ways :
> - by FEM Galerkin
> - by integration (Biot and Savart law)
>
> I am trying these calculations on a simple geometry (a troidal coil) and
> want to compare the results (hoping they will be the same).
>
> I can solve the Galerkin equations with a vector potential formulation
> (gauged by a spanning tree) and the result is perfect. However I have
> problems with GetDP's integral quantities...
>
> The .geo and .pro files are attached and here are my questions :
>
> -----------
> On the gmsh mailing list Christophe Geuzaine wrote (Sun, Apr 22, 2007) :
>
>> In an "Integral" quantity the coordinates of the "source" integration
>> point are denoted by XS[], YS[] and ZS[]. X[], Y[] and Z[] will give you
>> the coordinates of the "observation" point.
>
> OK, I managed to do something with $XS (I thought the source point
> would be implicitly taken, but this is not the case), but :
>
> GetDP : Error ('torus.pro' line 130): Unknown Function: XS
>
> are you really sure you have implemented XS[] ? or how can it be used ?
Yes. Both XS[] and $XS can normally be used, but I recommend using XS[],
as $XS has not been tested and is not guaranteed to be valid in all
expressions.
The "sign reversal" in D_inf comes from the fact that the elements in
your mesh are reversed in that region... Be careful to create your mesh
with normals pointing in the correct direction.
> (I have seen no example of $XS or XS[] on the web, the wiki or the GetDP
> mailing list)
> -----------
>
> There are several results which are weird or simply wrong :
>
> - as a test, I tried to calculate \int_{Coil} J_s : the result should be
> \vec 0 but something very different and weird is obtained (see a2.pos)
>
> (I think this point should really be clarified, because if it doesn't
> work, there is few chance that the rest will)
>
> - the direction of B2Z is reversed (although I think I carefully checked
> the signs of GradLaplace and the cross products)
>
> - B2Z should be equal to B1
>
> - does the integral quantity result depend on the FunctionSpace basis
> type used (BF_Edge or BF_Facet) ? it seems it does not.
>
> -----------
>
> It would be quite encouraging if someone could tell the correction which
> would make the file torus.pro work properly.
>
> Have a nice day,
>
> O.C.
>
--
Prof. Christophe Geuzaine
University of Liege, Electrical Engineering and Computer Science
http://www.montefiore.ulg.ac.be/~geuzaine