[Getdp] [GetDP] Calculation of an Integral quantity
Olivier Castany
castany at quatramaran.ens.fr
Sat May 5 17:59:16 CEST 2007
> thank you kindly for your reply. I took some time this morning to
> review your "Torus3D" example, trying to see if I could figure out
> what X vs. XS is. I noticed a couple of things that are not clear to me:
Hello,
first, a warning : the file torus3D.pro calculates two different
and independent things :
1) FEM Galerkin method exactly the same as in torus.pro (did
you look at it ?)
2) Integral quantites
I could have tried to make only the 2nd calculation, but after reading
Bernhard Kubicek's comments in Tower3DBiot, I thought it would produce
error messages if there were no "Equation" term, so I wrote 1) and 2)
in the same file. I have no time now to try and see if it is possible to
calculate only part 2).
(a warning about Tower3DBiot : I think Bernhard made a mistake and
should use ZS instead of Z ; in his example, however, this does not make
a huge difference ; I've mailed him)
> 1) In FunctionSpace, you define function spaces on "D_tot" and
> "CoilSection", in Formulation, you define an Equation in these, but
> you also use that FunctionSpace
^^^^
No : there are 3 function spaces : potentiel_vecteur_jauge,
potentiel_vecteur, champ_mag
> to define two Quantities that work on "Coil", namely "a2" and "B2".
^^^^
I don't understand that word in this context.
> How can a Quantity be defined on a
> region ("Coil") when it has no function space there?
"a2" belongs to the function space "potentiel_vecteur" => a2 lives on
D_tot (with other words : a2 is defined on D_tot)
The term "In Coil" is the integration domain of the source point :
a2( (X,Y,Z) \in D_tot ) = \int_{(XS,YS,ZS) \ in Coil} mu0 *
Laplace[]{3D} * J_s_source[]
(Laplace[]{3D} is a function of (X,XS,Y,YS,Z,ZS) and J_s_source[] is a
function of (XS,YS,ZS,NormalSource))
> 2) I did note your use of X vs XS, but I still do not understand. To
> begin with, you seem to use J_s only, defined on X, and not
> J_s_source, defined on XS. So what is the point of working with XS?
I do use "J_s_source" ! See the definition of the integral quantities.
Example :
{ Name a2 ; Type Integral ; NameOfSpace potentiel_vecteur ;
[ mu0 * Laplace[]{3D} * J_s_source[] ];
In Coil ; Jacobian JSur ; Integration I ; }
> Does XS only become meaningful if I use certain functions?
I think it is only meaningful in an integral quantity expression.
> Can I define where I want my XS to be? If so, how?
See my explaination of the term "In Coil" above.
> 3) The expression "Q(X,...) = \int_{XS,...} q(X,XS,...)" you mention
> below is pretty much what I am after, but I did not see where or how
> you implemented this in "Torus3D"?
In the definition of the integral quantities. See above.
Regards,
O.C.