[Getdp] Magnetodynamic 3D - Electromagnetic circuit element

[Christophe Geuzaine]

Florin CIUPRINA wrote:
> Hello,
> 
> I am still modeling the L-shape conductor (3D) but now in the magnetodynamic
> case (time harmonic and transient). I tried to use the a-v formulation with 
> edge elements for "a"
> and nodal elements with floating scalar potential on the terminals for "v".
> The boundary conditions I tried to impose are a = 0 on the whole boundary, 
> v = 1 on one terminal and
> v = 0 on the other one. Since edge elements are used for a, I did not 
> include the penalty term in the equation.
> I obtained the solution, BUT  with a = 0 in all the domain which is not 
> right (I think). 

Florin - that's consistent with your definition of the function space:

> FunctionSpace {
>   { Name Hcurl_a_Gauge; Type Form1;
>     BasisFunction {
>      // a = a  s  
>       //     e  e  
>       { Name se; NameOfCoef ae; Function BF_Edge;
>         Support DomainC_Mag ; Entity EdgesOfTreeIn[DomainC_Mag, StartingOn Surf]; }
>     }
>     Constraint {
>      //gauge condition ae = 0 on tree edges and on some boundaries
>       { NameOfCoef ae;
>         EntityType EdgesOfTreeIn; EntitySubType StartingOn;
>         NameOfConstraint GaugeCondition_a_Mag_3D; }
>     }
>   }
> 
> Constraint {
> { Name GaugeCondition_a_Mag_3D; Type Assign;
>     Case {
>       { Region DomainC_Mag ; SubRegion Surf; Value 0.; }
>     }
> }

which reads: "define degrees of freedom on the edges on a spanning tree
in DomainC_Mag, and set all these degrees of freedom to zero". This is
obviously not what you want...

A correct definition of the discrete vector potential involves the edges
of the _complement_ of the spanning tree. The easiest way to do this
is to define the vector potential everywhere, and use the constraint to
fix the dofs to zero on the edges of the tree (so that only the edges of
the complement lead to actual unknowns).

Christophe

-- 
Christophe Geuzaine

Tel: (626) 395-4552    http://www.geuz.org
Fax: (626) 578-0124    mailto:geuzaine at acm.caltech.edu