[petsc-users] node DG with DMPlex

[Yann Jobic]

Hi matt,

Le 3/17/2020 à 4:00 PM, Matthew Knepley a écrit :
> On Mon, Mar 16, 2020 at 5:20 PM Yann Jobic <yann.jobic at univ-amu.fr 
> <mailto:yann.jobic at univ-amu.fr>> wrote:
> 
>     Hi all,
> 
>     I would like to implement a nodal DG with the DMPlex interface.
>     Therefore, i must add the internal nodes to the DM (GLL nodes), with
>     the
>     constrains :
>     1) Add them as solution points, with correct coordinates (and keep the
>     good rotational ordering)
>     2) Find the shared nodes at faces in order to compute the fluxes
>     3) For parallel use, so synchronize the ghost node at each time steps
> 
> 
> Let me get the fundamentals straight before advising, since I have never 
> implemented nodal DG.
> 
>    1) What is shared?
I need to duplicate an edge in 2D, or a facet in 3D, and to sync it 
after a time step, in order to compute the numerical fluxes 
(Lax-Friedrichs at the beginning).
> 
>        We have an implementation of spectral element ordering 
> (https://gitlab.com/petsc/petsc/-/blob/master/src/dm/impls/plex/examples/tutorials/ex6.c). 
> Those share
>        the whole element boundary.
> 
>    2) What ghosts do you need?
In order to compute the numerical fluxes of one element, i need the 
values of the surrounding nodes connected to the adjacent elements.
> 
>    3) You want to store real space coordinates for a quadrature?
It should be basically the same as PetscFE of higher order.
I add some vertex needed to compute a polynomal solution of the desired 
order. That means that if i have a N, order of the local approximation, 
i need 0.5*(N+1)*(N+2) vertex to store in the DMPlex (in 2D), in order to :
1) have the correct number of dof
2) use ghost nodes to sync the values of the vertex/edge/facet for 
1D/2D/3D problem
2) save correctly the solution

Does it make sense to you ?

Maybe like 
https://www.mcs.anl.gov/petsc/petsc-current/src/ts/examples/tutorials/ex11.c.html
With the use of the function SplitFaces, which i didn't fully understood 
so far.

Thanks,

Yann

> 
>        We usually define a quadrature on the reference element once.
> 
>    Thanks,
> 
>      Matt
> 
>     I found elements of answers in those threads :
>     https://lists.mcs.anl.gov/pipermail/petsc-users/2016-August/029985.html
>     https://lists.mcs.anl.gov/mailman/htdig/petsc-users/2019-October/039581.html
> 
>     However, it's not clear for me where to begin.
> 
>     Quoting Matt, i should :
>     "  DMGetCoordinateDM(dm, &cdm);
>         <Set field information into cdm instead of dm>
>        DMCreateLocalVector(cdm, &coordinatesLocal);
>        <Fill in higher order coordinate values>
>        DMSetCoordinatesLocal(dm, coordinatesLocal);"
> 
>     However, i will not create ghost nodes this way. And i'm not sure to
>     keep the good ordering.
>     This part should be implemented in the PetscFE interface, for high
>     order
>     discrete solutions.
>     I did not succeed in finding the correct part of the source doing it.
> 
>     Could you please give me some hint to begin correctly thoses tasks ?
> 
>     Thanks,
> 
>     Yann
> 
> 
> 
> -- 
> What most experimenters take for granted before they begin their 
> experiments is infinitely more interesting than any results to which 
> their experiments lead.
> -- Norbert Wiener
> 
> https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>