Symmetric boundary condition

[simbilod]

Hello kinnala and other users/developers, great library!

Does there already exist a way to define symmetric (mirror) boundary conditions (for example as described here)?

If not, is there something can we easily modify to enable this?

[kinnala]

It is possible to impose such symmetry conditions. Usually symmetry conditions are implemented in terms of other basic boundary condition types (Neumann or Dirichlet). The practical implementation depends, to some extent, on which governing equation you are interested in. Is it linear elasticity as in your link?

[kinnala]

As the basis functions of Nedelec elements are vector-valued, it may not be possible to set specific components to zero. I tried to find information on how symmetry conditions are implemented for Nedelec elements but I was not able to find anything. I will do a more careful review at some point. I think the way it is done for $H^1$ conforming elements and $H(curl)$ conforming elements will be different.

[simbilod]

Sounds good! I'm not extremely familiar with the FEM literature, so if you have anything to recommend me to look into I can do that too

[kinnala]

I have a background in solid mechanics so I can intuitively understand how symmetry conditions work there. The point is to not allow any displacement in the normal direction with respect to the symmetry plane as otherwise there would be a gap in the material over the symmetry plane. The tangential direction should be traction free as there are not any external forces acting there. These will involve a dot product of the displacement and the normal vector and the dot product of the traction vector and the normal vector.

I have no intuition for electromagnetism, I studied just one course more than ten years ago, and it involved no numerics. According to this source, the symmetry conditions in electromagnetism may include the cross product of the field and the normal vector: https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.6088 I am not sure how this can be physically interpreted but perhaps it makes more sense to you?

[HelgeGehring]

It seems to me that we just find the second eigenmode with the current boundary conditions, right?
If we just stick with the boundary conditions of "full" I get exactly the mode we see for full.

I somewhen thought quite a bit about this (DOFs of nedelec element = 0 at the interface => tangential vector at interface = 0, right?) for doing perflectly magnetic / electric conductors, but I didn't write it down yet :/

[kinnala]

Yes, Nedelec DOFs correspond to the tangential component of the vector field.