Forced Constant Potential

NGSolve
1

Hello everyone,
in an eigenvalue/vector problem I need a uniform potential on a particular surface (there are also other dofs). If it weren’t for the eigenvalue setting, I would define a dirichlet bc.
Can I implement this via periodicity; that I would define a master vertex with all other surface vertices as slaves?
Best to everyone

2

Hi,
with periodic it is not possible as periodic vertex pairs are not allowed to be in the same element.
I think it should be possible by defining the boundary dirichlet and introducing one more variable with a number fespace and using a Gridfunction that is one on the boundary.
Best
Christopher

3

Thank you very much for the reply;
is there an example out there how the FESpace is then put together for this degree of freedom. There is ample examples of how to define the GridFunction.
Best

4

One more question; can the resulting matrix obtained by taking the sum of the rows/cols of the corresponding dofs?

5

Hi,
a quick solution is to add a term

10**8 * grad(u.Trace()) * grad(v.Trace()) * ds("bnd")

to the stiffness matrix. It penalizes the variation of the eigenfunction on the conducting boundary.

Joachim

6

And also thank you; no luck so far however; my guess is that in my case it is an interior boundary. Additionally I have to use .Deriv() since the potential is not the only degree of freedom

(*u, phi*) = fes.TrialFunction()
...
stiff += 1E8*(phiV.Trace().Deriv() * phiU.Trace().Deriv())*ds('elec')

I also tried to penalize the gradient within the domain of the electrode without success

el_cf = CoefficientFunction([1 if bnd == 'elec' else 0 
                                      for bnd in mesh.GetBoundaries()])
U_el = GridFunction(fePhi)
U_el.Set(el_cf, BND)
...
10E8*(phiV.Deriv() * phiU.Deriv())*U_el*dx

Unsuccessful insofar as it appears to be ignored (same result without the line).
Any help is appreciated;
Best to all

7 
u.Set(1, BND)

only sets on Dirichlet boundaries (legacy reasons) use

u.Set(1, definedon=mesh.Boundaries(bndname))

instead