[Getdp] Von Neumann misconception?

[John_V]

Thanks Lars. If I understand you, you're telling me that my answer A was the
right one. (Eimposed was a very simple function in my case. It was
constant.) But in my solution, the field at UpperEndCap is much different
from Eimposed. Why is that?

I am suspecting the real answer is B. This suspicion is, however, based only
on observation. I don't know whether this makes sense in terms of how the
program is supposed to operate. Domain_Ele does not exclude UpperEndCap.
That is, the nodes on UpperEndCap (a surface) are also nodes of Domain_Ele,
which is the entire mesh. Does that offer a way to explain why the field is
not what I expected?

John

On Thu, Aug 4, 2011 at 2:23 AM, Lars Rindorf <lrf at teknologisk.dk> wrote:

>  Hi John****
>
> ** **
>
> The Neumann (von Neumann is a different mathematician) boundary condition
> fixes the ‘influx’ grad(V) normal to the boundary, and it arises when
> grad(V) = -E is known and can be replaced by a function, such as Eimposed. A
> dirichlet boundary condition, e.g. V=0, fixes the magnitude.****
>
> ** **
>
> Be aware that in the formulation the ‘Eimposed’ is the normal component of
> the incoming field/flux and it is thus a scalar not a vector.****
>
> ** **
>
> KR Lars****
>
> ** **
>
> *Fra:* getdp-bounces at ace20.montefiore.ulg.ac.be [mailto:
> getdp-bounces at ace20.montefiore.ulg.ac.be] *På vegne af *John_V
> *Sendt:* 3. august 2011 14:21
> *Til:* getdp at geuz.org
> *Emne:* [Getdp] Von Neumann misconception?****
>
> ** **
>
> Consider an electrostatic problem in a cylindrical volume, bottom end cap
> (surface) constrained to V=0, source terms in some volume elements, and top
> end cap with a von Neumann constraint implemented as shown in the
> formulation below. Does the 3rd Galerkin term (the von Neumann term)****
>
> a) Require that the electric field through the upper end cap be equal to
> Eimposed?
> b) Require that the electric field through the upper end cap be equal to
> the sum: field produced by charges in SourceDomain + Eimposed?
> c) Something else?****
>
>
> Formulation {
>   { Name Electrostatics_v; Type FemEquation;
>     Quantity {
>       { Name v; Type Local; NameOfSpace Hgrad_v_Ele; }
>     }
>     Equation {
>       Galerkin { [ epsr[] * Dof{d v} , {d v} ]; In Domain_Ele;
>                  Jacobian Vol; Integration GradGrad; }
>       Galerkin { [ -q[]*chargeUnit/eps0/ElementVol[] , {v} ]; In
> SourceDomain;
>                  Jacobian Vol; Integration GradGrad; }
>       Galerkin { [ Eimposed , {v} ]; In UpperEndCap;
>                  Jacobian Sur; Integration GradGrad; }
>     }
>   }
> }
>
> The mesh is a cylindrical volume oriented along z. Domain_Ele refers to all
> volume elements of my mesh. SourceDomain is a set of volume elements in
> which there are charges. (These are near the lower end cap of the
> cylindrical mesh.) The 3rd term was meant to impose my von Neumann
> condition. When I wrote it I thought I was doing (a) above, but the result
> suggests otherwise.
>
> John****
>
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