[Getdp] [GetDP] Calculation of an Integral quantity

[Olivier Castany]

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 :

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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 ? 
(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.

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