Nedelec Elements for unstructured adaptively refined meshes

[Artur Safin]

Dear community,

In the near future, I will need to solve a curl-curl problem ∇×(∇×u)=u. I will have to use an unstructured grid (gmsh-generated) that is also adaptively refined. From what it seems, the appropriate class for such problems (Nedelec_FE) is incomplete, and so thought I'd ask as to how I should proceed.

1) Can FE_Nedelec work for unstructured adaptively refined meshes (for linear polynomials)?

2) There is a new Nedelec FE class (pull 2240) that is currently being merged into the master branch - should I use that instead? (And also, does it support adaptive meshes?)

Thank you,

Artur

[Bruno Turcksin]

Artur,

On Wednesday, May 9, 2018 at 8:51:37 PM UTC-4, Artur Safin wrote:

1) Can FE_Nedelec work for unstructured adaptively refined meshes (for linear polynomials)?

2) There is a new Nedelec FE class (pull 2240) that is currently being merged into the master branch - should I use that instead? (And also, does it support adaptive meshes?)

The current version of FE_Nedelec should only be used for cartesian mesh. The new class is able to able to use unstructured meshes but it does not support hanging nodes and therefore you cannot do adaptive mesh refinement. If you need adaptive mesh refinement, you will need to add the capability to treat hanging nodes to the class.

Best,

Bruo

[Matthias Maier]

On Thu, May 10, 2018, at 08:10 CDT, Bruno Turcksin <bruno.t...@gmail.com> wrote:

> The current version of FE_Nedelec should only be used for cartesian mesh.

I have had no problems on unstructured, locally refined 2D meshes with
our FE_Nedelec element so far. (With verified correct results when
comparing against analytic solutions.)

We keep repeating that the current element only works on Cartesian
meshes, but I am not sure whether this is actually true.

Best,
Matthias

[Bruno Turcksin]

2018-05-10 16:35 GMT-04:00 Matthias Maier <tam...@43-1.org>:

We keep repeating that the current element only works on Cartesian
meshes, but I am not sure whether this is actually true.

Many people have reported problems see this thread for example https://groups.google.com/forum/#!searchin/dealii/nedelec%7Csort:date/dealii/ao-bi_Nh7gc/jHq1qMJlAgAJ If I remember correctly, J-P couldn't make Nedelec work for his problem a few months ago.

Best,

Bruno

[Matthias Maier]

On Thu, May 10, 2018, at 15:41 CDT, Bruno Turcksin <bruno.t...@gmail.com> wrote:

> Many people have reported problems see this thread for example
> https://groups.google.com/forum/#!searchin/dealii/nedelec%7Csort:date/dealii/ao-bi_Nh7gc/jHq1qMJlAgAJ
> If I remember correctly, J-P couldn't make Nedelec work for his problem a
> few months ago.

The problem in the thread you cited is for 3D. I am happy to update our
disclaimer for the class.

I am just saying that our statement:

"For the moment, it is safe to use the element on globally refined
meshes with consistent orientation of faces."

with the addition "in 2D" and for "lowest and second order" is true :-)

Best,
Matthias

[Bruno Turcksin]

2018-05-10 16:52 GMT-04:00 Matthias Maier <tam...@43-1.org>:

with the addition "in 2D" and for "lowest and second order" is true :-)

Yeah you are right, it's always in 3D that people have problems.

Bruno

[Jean-Paul Pelteret]

On 10 May 2018, at 22:41, Bruno Turcksin <bruno.t...@gmail.com> wrote:

If I remember correctly, J-P couldn't make Nedelec work for his problem a few months ago.

Yes, that’s correct. I was working on a magneto-static problem in 3d, and wasn’t able to achieve sensible results. That said, I couldn’t say for certain that this wasn’t due to something that I was doing wrong (I had implemented a specialised strategy for gauging the system) so I wouldn’t say its fair to pass judgement based on my experience.

J-P

[Wolfgang Bangerth]

> The problem in the thread you cited is for 3D. I am happy to update our
> disclaimer for the class.
>
> I am just saying that our statement:
>
> "For the moment, it is safe to use the element on globally refined
> meshes with consistent orientation of faces."
>
> with the addition "in 2D" and for "lowest and second order" is true :-)

The problem is with cells that have non-standard face orientation. This can't
happen in 2d, but it happens for some complex 3d meshes. It's so difficult to
debug these issues because the meshes need to be sufficiently complicated that
drawing pictures is no longer possible...

Best
W.


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