[Getdp] How to properly couple Magnetostatic and Electrostatic problem?

[Christophe Geuzaine]

Christophe Trophime wrote:
> Starting from the Magnetostatics examples I try to compute the magnetic
> potential from the resolution of the electrical potential in the
> conductors :
> 
>   { Name MagSta_a_3D; Type FemEquation;
>     Quantity { 
>       { Name a ; Type Local; NameOfSpace Hcurl_a_MagSta_3D; }
>       { Name ur ; Type Local  ; NameOfSpace Hregion_u_3D ; }
>     }
>     Equation {
>       Galerkin { [ nu[] * Dof{d a} , {d a} ]; 
>                  In Vol_Mag; Integration GradGrad; Jacobian Vol; }
>       Galerkin { [ -sigma[] * {d ur} , {a} ]; 
>                  In Vol_S_Mag; Integration GradGrad; Jacobian Vol; }
>     }
>   }
> 
> where ur is defined as :
> FunctionSpace {
> 
>   { Name Hregion_u_3D ; Type Form0 ;
>     BasisFunction {
>       { Name sr ; NameOfCoef ur ; Function BF_Node ;
>       Support Domain_Elec ; Entity NodesOf[ All, Not
> Domain_Electrode ] ; }
>       { Name sg ;NameOfCoef ug ; Function BF_GroupOfNodes ;
>         Support Domain_Elec ; Entity GroupsOfNodesOf
> [ Domain_Electrode ] ; }
>     }
>     GlobalQuantity {
>       { Name V ; Type AliasOf        ; NameOfCoef ug ; }
>       { Name I ; Type AssociatedWith ; NameOfCoef ug ; }
>     }
>     Constraint {
>       { NameOfCoef ur ; 
>         EntityType NodesOf ; NameOfConstraint FixedVoltage ; }
>       { NameOfCoef V ;
>         EntityType GroupsOfNodesOf ; NameOfConstraint
> FixedGlobalVoltage ; }
>       { NameOfCoef I ;
>         EntityType GroupsOfNodesOf ; NameOfConstraint
> FixedGlobalCurrent ; }
>     }
>   }
> }
> 
> and 
> 
>   { Name Electric_Conduction ; Type FemEquation ;
>   Quantity {
>     { Name ur ; Type Local  ; NameOfSpace Hregion_u_3D ; }
>     { Name I ; Type Global ; NameOfSpace Hregion_u_3D [I] ; }
>     { Name V ; Type Global ; NameOfSpace Hregion_u_3D [V] ; }
>   }
>   Equation {
>     Galerkin { [ sigma[] * Dof{d ur} , {d ur} ] ; In Domain_Elec ;
>     Jacobian Vol ; Integration GradGrad ; }
> 
>     GlobalTerm { [ Dof{I} , {V} ] ; In Domain_Electrode ; }
>   }
>   }
> 
> The resolution gives the following error :
> 
> Operation : Generate[A]
> Solver    : Loading parameter file 'Sys_Mag.par'
> Info      : Setting System {A,b} to zero
> Error     : Substraction of different quantities: Vector - Scalar
> 
> As far as I understand right the error indicates that ur is not in a
> "right" functionnal space.
> 
> How can I project "sigma[] * {d ur}" to get the corresponding {j} in the
> right functionnal space?
> 

Could you send all the .pro files as well as a small mesh?



> 
> 
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-- 
Christophe Geuzaine
Assistant Professor, Case University, Mathematics
http://www.case.edu/artsci/math/geuzaine