[Getdp] coupling electrokinetic and Magnetostatic problems

[François Henrotte]

Hello Marco,


Yes.
The first three terms in the formulation below
describe equations associated with the test functions
of the edge unknowns (or node unknowns in 2D)
of the magnetic vector potential field ‘a’
in the whole domain of computation ‘Domain’.
They express the weak form fo the Euler-Lagrange equation:

curl (nu curl a) + sigma( dadt + grad u) = 0 (curl h = j)


The next 2 terms are associated with the test functions
of the node unknowns of the scalar electric potential ‘v’,
only for nodes in the conducting domain ‘DomainC’.
They express the weak form fo the Euler-Lagrange equation:

div ( sigma( dadt + grad u) ) = 0 (div j=0)

By analyzing the ‘Quantity’ section of the ‘Formulation’ field,
which I reproduce below

    Quantity {
      { Name a  ; Type Local ; NameOfSpace Hcurl_a_3D ; }

      { Name v  ; Type Local  ; NameOfSpace Hregion_u_3D ; }
      { Name U  ; Type Global ; NameOfSpace Hregion_u_3D [U] ; }
      { Name I  ; Type Global ; NameOfSpace Hregion_u_3D [I] ; }
    }


together with the informations contained
in the « FunctionSpace » section and the declared « Constraints »  acting on it,
GetDP is able to decide which Dofs are fixed
and which are unknowns (and then associated with a test function).
This is all automatic.
That is the reason why it is enough in the Formulation description
to give the weak form of the equations you want to solve.

Regards,

Fr.


Equation {
      Galerkin { [ nu[] * Dof{d a} , {d a} ] ;
        In Domain ; Jacobian Vol ; Integration I1 ; }
      Galerkin { DtDof[ sigma[] * Dof{a} , {a} ] ;
        In DomainC ; Jacobian Vol ; Integration I1 ; }
      Galerkin { [ sigma[] * Dof{d v} , {a} ] ;
        In DomainC ; Jacobian Vol ; Integration I1 ; }

      Galerkin { DtDof[ sigma[] * Dof{a} , {d v} ] ;         // <====== A1
       In DomainC ; Jacobian Vol ; Integration I1 ; }
      Galerkin { [ sigma[] * Dof{d v} , {d v} ] ;               // <====== A2
        In DomainC ; Jacobian Vol ; Integration I1 ; }

      GlobalTerm { [ Dof{I} , {U} ] ; In SurfaceElecWithI ; }

      Galerkin { [ - js0[] , {a} ] ; In DomainS ;
        Jacobian Vol ; Integration I1 ; }
    }

I don't understand how A1 and A2 can be part of the same integral. I mean, based on the micro strip tutorial,
 every Galerkin{....} term belonging to Equation{...} is added up and this sum is then made equal to zero. And this equation should hold for a single test function.
But here A1 and A2 have a test function different from the other terms. Does this mean that GetDP generates automatically two equations? One for test functions a' and one for test functions v’?






I'm lost, help please :D

Marco
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--
François Henrotte Dr Ir - francois.henrotte at uclouvain.be<mailto:francois.henrotte at uclouvain.be> - francois.henrotte at uliege.be<mailto:francois.henrotte at uliege.be>
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