[Getdp] coupled electrical field - particle densities

Reinhold Ingo ingo.reinhold at s2001.tu-chemnitz.de
Tue Nov 14 18:27:37 CET 2006

Dear all,

I'm not too familiar with GetDP and hope to get some answers by  
posting my problem here.

I'm trying to compute a problem with coupled electrical field and  
particle densities. From the literature it is suggested that for  
example electron densities in partial discharges are computed by  
something like

	dt(ne)=div(D grad(ne))-div( ve*ne)+C*ne

The electrical field is then
	div( epsr grad(phi))-e/eps0*ne=0

However what confuses me now is, that when I'm trying to compute the  
problem in GetDP I run into a lot of problems. Maybe I'm doing  
something wrong in the formulation.

If I'm right the second equation gives a weak formulation of

	Galerkin { [ epsr[] * Dof{d v} , {d v} ]; In Volume; Jacobian Vol;  
Integration Int; }
	GlobalTerm { [ -elemc*Dof{NE}/(eps0) , {V} ]; In Boundary;}

Since NE is defined as a GlobalQuantity my problem of understanding  
is now how to arrange the first equation in such a way, that both  
work together in a non-linear algorithm, even though the density is  
in the plane, while NE in the above given formula is only at the  
boundary and set up in a function space like this

	FunctionSpace {
	{ Name Elec; Type Form0;
	BasisFunction {
	{ Name sn ; NameOfCoef vn ; Function BF_Node ; Support Region 
[{Volume}] ; Entity NodesOf[ All,Not Boundary] ; }
     	{ Name sf ; NameOfCoef vfu ; Function BF_GroupOfNodes ; Support  
Volume ; Entity GroupsOfNodesOf[Boundary] ; }
    	 GlobalQuantity {
			{ Name GlobalElectricPotential ; Type AliasOf        ; NameOfCoef  
vfu ; }
			{ Name GlobalElectronDensity   ; Type AssociatedWith ; NameOfCoef  
vfu; }
	Constraint {
    	 { NameOfCoef GlobalElectronDensity ; EntityType  
GroupsOfNodesOf ; NameOfConstraint ElectronDensity; }
    	 { NameOfCoef GlobalElectricPotential ; EntityType  
GroupsOfNodesOf ; NameOfConstraint ElectricScalarPotential ; }	}

My guess was that the electron density is then calculated using

	Galerkin { Dt[ Dof{NE} , {NE} ]; In Volume; Jacobian Vol;  
Integration Int; }
	Galerkin { [ Dof{NE}*we , {d ne} ]; In Volume; Jacobian Vol;  
Integration Int; }
	Galerkin { [ -De*Dof{d ne} , {d ne} ]; In Volume; Jacobian Vol;  
Integration Int; }
	Galerkin { [ -C*Dof{NE} , {NE} ]; In Volume; Jacobian Vol;  
Integration Int; }

but didn't succeed.

It would be really great if someone could give me hint how to  
formulate it.

Thanks in advance and nice greetings from Chemnitz,


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