[dune-pdelab] Access to another cell in alpha_skeleton

[Dominic Kempf]

Hey Jonas,

welcome to PDELab! I wished I had a better welcoming gift to you...

I am assuming that the scheme you are trying to implement is something like
Figure 1b from
"Nonlinear two-point flux approximation for modelingfull-tensor effects in
subsurface flow simulations"
by Chen et al. - correct me if I am wrong.

We get this question and variations of it a lot, and unfortunately the most
adequate answer is:
The assumption that a facet integral only depends on the two neighboring
cells
is built quite deeply into the PDELab assembler. That being said, there is
no clean solution to
your problem in PDELab.

I know that DuMux (www.dumux.org, a downstream project) has treated that
problem before.
I am not sure they are relying on the PDELab assembler in their
implementation, but it is worth
asking them.

Of course, things can always be hacked. Most probably one can do something
with precomputation
of all flux values at all intersection mid points, but I am not sure about
the details (e.g. I have no
clues about how jacobians for such a system could be computed).

Best,
Dominic

On Mon, Jul 6, 2020 at 3:30 PM Jonas Beddrich <jonas.beddrich at gmail.com>
wrote:

> Hi everyone,
>
> I'm looking for a method to access the values of cells in the
> alpha_skeleton function of my local operator in addition to the values of
> the inside and outside cell of the intersection.
>
> The nonlinear Two Point Flux Approximation I'm currently working on
> requires information about 4 cells to compute the flux through each
> intersection. So in addition to the inside and outside cell two additional
> cells m and k are required. The cells m and k are dependent on the
> intersection, the inside and outside cell as well as problem parameters.
> Right now I can determine the index of those cells and then get the
> corresponding elements by iterating over the grid.
>
> Sadly, I haven't found an efficient way to access the values of these
> cells, since alpha_skeleton only gets the local vectors and local function
> spaces of the inside and outside cell. But I guess I'm not the only person
> encountering this problem. Can anyone give me a hint on how to solve this?
>
> Best regards,
> Jonas
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