Martin,
I'm not sure what happened to my previous reply, it seems to have been
deleted somehow.
I haven't been able to implement the 1D version of this method in deal.ii
yet, but I did do a prototype in Julia which leads me to believe it's
simpler than I anticipated. However, one important detail eludes me for the
deal.ii implementation: how to iterate over one "slice" of a tensor product
quadrature rule.
In essence, for a quadrature point $q_{i,j,k}$, the two-point volume flux
term wants a contribution from all of the quadrature points sharing one
index, namely all of the points $q_{i,j,m}$ for example.
Would you be able to share a pointer to documentation on how the
FEEvaluation class numbers the quadrature points in a tensor-product rule?
If I know that then I believe I can write a hacky loop that does the
appropriate thing by manually combining the quadrature rule and
FiniteElement<dim=1>.
Best,
-Jack
On Wednesday, April 24, 2024 at 1:28:07 PM UTC-7 Martin Kronbichler wrote:
> Dear Jack,
>
> Two-point fluxes are something we have not yet included in deal.II. I
> would be very interested if we could realize this feature. I must admit
> that I did not yet try to understand the complete formula in the link you
> provided, but in fact it should be possible to implement this with the
> internal evaluators used by FEEvaluation very efficiently. Would you be
> willing to share the FEValues variant, it is enough to provide it in 1D. I
> did work with the Trixi code before, but did not yet look into the
> algorithms, so I would be very curious to learn the details. My initial
> approach would be to encode the full D_split matrix to be fed into the
> tensor product evaluators in the internal namespace, and then add the
> respective boundary fluxes. Once we have a basic version, we can think
> about making the interface nicer.
>
> Best,
> Martin
>
>
> Am 23.04.24 um 17:19 schrieb Jack Coughlin:
>
> I am interested in using the deal.ii matrix-free infrastructure to
> implement an entropy-stable DG method. The entropy stable family of methods
> uses an interesting variation, where the volume flux is actually a
> consistent two-point flux function (similar to the numerical flux).
>
> I've attached a screenshot of the formula in question, which is taken from
> this
> documentation page
> <https://trixi-framework.github.io/Trixi.jl/stable/tutorials/DGSEM_FluxDiff/#DGSEM-with-flux-differencing>.
>
> I've also attached a review of the method.
>
> As far as I can tell, to do this you would need to be able to tell a class
> like FEEvaluation to integrate a given submission only for one test
> function. I think I can see how to do this integration manually with
> FEValues, but it would be nice to take advantage of the matrix-free
> infrastructure if possible.
>
> Thank you,
> -Jack C
>
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