[Dune] Using PDELab's alpha_skeleton with larger stencil?

[Bryan Doyle]

Hi Christoph,
Thank you for the prompt response! As a follow-up question, were you able
to find a work around when you encountered this limitation? Were there any
specific strategies that you looked into?

In my particular case, I only have a handful of integrals of the form I
described above, so I was thinking that it may be possible to add in a
block of code (possibly somewhere in the Newton solver?) that looped over
the mesh edges after each iteration and added these terms to the residual
vector, outside of the calls to alpha_skeleton. Would this be something
that (a) could work in theory, and (b) could be implemented without
developer-level knowledge of the DUNE code?

Thank you for your time,
Bryan

On Mon, Sep 10, 2018 at 11:40 PM Christoph Grüninger <foss at grueninger.de>
wrote:

> Hi Bryan,
> as far as I know, this is not possible.
>
> > FE and FV schemes requiring at most face-neighbors
>
> https://www.dune-project.org/modules/dune-pdelab/
>
> The rationale is, that this limitation keeps the interface clean, the
> number of evaluations low and the sparsity pattern known.
>
> Bye
> Christoph, who struggled with this limitation already
>
> Am 11.09.2018 um 04:09 schrieb Bryan Doyle <btd2 at rice.edu>:
>
> Hello,
> I am using DUNE's PDELab, and noticed that in the alpha_skeleton calls,
> only 2 coefficient vectors are available: x_s and x_n. This implies that
> only the unknowns evaluated on the self and neighbor cells are available
> for use in alpha_skeleton's calculations. Suppose my weak form had an
> integral over an edge which depended on the unknowns evaluated on cells
> other than the self and neighbor elements; would it be possible to
> implement this using PDELab?
>
> As a more concrete example, assume I have a uniform square grid, with
> elements E_1 and E_2 which do not share an edge. Suppose I wish to calculate
> \int_e u_1*u_2,
> where u_1 and u_2 are the unknowns evaluated in the centers of elements
> E_1 and E_2, respectively, and e is some edge of E_1. Is calculating this
> integral possible using PDELab's alpha_skeleton function, or is there
> another way to do so?
>
> Any advice or input would be greatly appreciated!
>
> Thank you for your time,
> Bryan
>
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