Dear Martin,
The conversations for the two point flux entropy stable DG seem to be
deleted. However this is an important topic (for strong shocks etc). Could
this be done with the Matrix-Free / FEEvaluation routines or would one need
to do something similar to step-69. I prefer FE_DGQ with Gauss-Lobatto
quadrature and the highly efficient routines therein. Naively speaking, we
would need the following type of pseudo code (for 1D) :
Form split_derivative_matrix = D_split[q,q1] for q,q1 in [0....N];
(diagonal entries of D_split are zero)
for q in [0:N]: // q and basis same for Gauss-Lobatto quadrature
get u[q] // dof value
for q1 in [q+1:N] // Diagonal contribution is 0
get u1[q]
F[u,u1] = two_point_flux(u,u1) // This will be symmetric in
u,u1
u_q += D_split[q,q1]*F[u,u1]
u_q += D_split[q1,q]*F[u1,u] // Symmetric so F[u,u1] =
F[u1,u]
Maybe a more sophisticated algorithm with Tensor / Hadamard products could
be formulated ?
For high performance, can the above be done efficiently in the deal.ii
matrix free framework ? And if so how ?
Regards,
Rochan
On Wednesday, April 24, 2024 at 3:28:07 PM UTC-5 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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