Hanging node constraints in FE_NedelecSZ

[Vinta Yinda Wang]

Hello everyone:

I was trying to do adaptive mesh refinement in 2D-electromagnetic problem following the program provided in step-81. The refinement procedure is refererred to step-27, where I implement the FESystem of real and imaginary FE_NedelecSZ part in hp::FECollection class.

After the first refinement step, I failed to make the hanging node constraint .

The violated condition is detailed as

The finite element for which you try to obtain hanging node
    constraints does not appear to implement them.

Has anyone encountered the same problem before? I am not sure whether is the problem in my code, or the hanging node constraint hasn't been implemented in FE_NedelecSZ?

Thank you all!

[Wolfgang Bangerth]

On 10/23/22 01:46, Vinta Yinda Wang wrote:
> I was trying to do adaptive mesh refinement in 2D-electromagnetic problem
> following the program provided in step-81. The refinement procedure is
> refererred to step-27, where I implement the FESystem of real and imaginary
> FE_NedelecSZ part in hp::FECollection class.
> After the first refinement step, I failed to make the hanging node constraint .
> The violated condition is detailed as

> *The finite element for which you try to obtain hanging node

>     constraints does not appear to implement them.

> *

> Has anyone encountered the same problem before? I am not sure whether is the
> problem in my code, or the hanging node constraint hasn't been implemented
> in FE_NedelecSZ?

Vinta: The latter. They are simply not yet implemented. But you can of course
help with that and we will be very happy to guide you to what needs to be
implemented!

Best
W.

--
------------------------------------------------------------------------
Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/

[Alexander]

Dear Vinta

for 2-D, you could consider resorting to FE_Nedelec, which supports hanging nodes. In contrast to the 3-D case, FE_Nedelec should work even for (some) non-standard grids in 2-D.

Best

Alexander

[Sebastian Kinnewig]

Hello everyone, 

I recently finished my implementation of hanging nodes for the FE_NedelecSZ class with arbitrary polynomial degrees for the 2-D and 3-D cases. I will submit my implementation soon to deal.II on GitHub, but as the implementation was quite cumbersome and shall be part of my dissertation I want to publish my implementation along with a paper (or at least a preprint). At the moment that paper is my main priority, therefore It shouldn't take too long until I will publish my code.

In the meantime, I would suggest the same workaround as Alexander.

Best,
Sebastian

[Vinta Yinda Wang]

Thank you Wolfgang and thank you Alexander!

In the Todo list of FE_Nedelec, 3-D cases ought to be carefully treated, because (from my understanding) some complex geometries in 3-D with non-standard grids (maybe unstructed or distorted initially) will introduce sign conflict issues present in traditional Nédélec elements that arise from the edge and face parameterization. But for some not-so-complicated meshes and geometries, it might still work?

Best 

Vinta

[Sebastian Kinnewig]

Yes, the FE_Nedelec elements will work for not-so-complicated meshes, for example, a simple cube will work just fine. 

Best,
Sebastian

[Vinta Yinda Wang]

Thank you Sebastian and thank you for your new contribution. I will keep on focusing on your paper for better understanding of this work!

So if the 3-D cases are consisted of structed meshes, the oritention is, all-appearance, not conflicted, the computation of such mesh works as well as the adaptive refined one?

Best,

Vinta