Felix,
I try to solve an Eigenvalue Problem (similar to the scalar-valued step-36) in
Electrodynamics, namely find the Eigenmodes of a Spherical waveguide. The
differential equation you try to solve there is the same as in the example in
this document about Nedelec's Finite Elements (nedelec.pdf
<http://www.math.chalmers.se/~stig/underv/doktorandkurs/FEM/200607/nedelec.pdf>),
namely curl(curl(E)) = omega^2*E. Now, for 2 spacial dimensions using Nedelec
Elements with two in-plane Vector components you only calculate TE
(Transversal Electric) modes, but this works fine. If I want to calculate the
TM (Transversal Magnetic) modes, I THINK (please feel free to lecture me) I
should use the differential equation for B, namely curl(curl(B)) = omega^2*B,
but for B the normal components are required to be continuous, so I should use
Raviart_Thomas Elements instead of Nedelec and use the Boundary condition of
vanishing normal components, i.e. project_boundary_values_div_conforming(...).
This can't be correct. The solutions of the curl-curl equation are in H_curl
and have continuous tangential component but possibly dicontinuous normal
components. You will not be able to impose normal boundary conditions.
This is just changing 2 lines in the Code, but gives the error below at
runtime (The Code is attached. As Error happens quite early in the
make_grid_and_dofs function and the code is very much tutorial-like, I hope it
is readable).
This is interesting, but independent of the issue above. Can you try to come
up with as small a program that shows this bug? If so, can you open a bug
report at
https://github.com/dealii/dealii/issues
for it?
Additional question: is there a possibilty to use 3d-Nedelec Elements on a 2D
geometry, or should I use an FE_System with a Nedelec Element and a FE_Q? In
this case, It seems I have to reformulate the curl operator, which I'm not
overly keen on...
I'm not sure I understand what you mean by "use 3d-Nedelec elements on a 2d
geometry". Can you elaborate?
Cheers
W.
--
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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