[petsc-users] node DG with DMPlex

[Matthew Knepley]

On Wed, Mar 18, 2020 at 12:58 PM Yann Jobic <yann.jobic at univ-amu.fr> wrote:

> 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).
>

I should have been more specific, but I think I see what you want. You do
not "share" unknowns between cells,
so all unknowns should be associated with some cell in the Section.

You think of some cell unknowns as being "connected" to a face, so when you
want to calculate a flux, you need
the unknowns from the adjacent cell in order to do it. In order to do this,
I would partition with overlap=1, which
is what we do for finite volume, which has the same adjacency needs. You
might also set


https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/DM/DMSetAdjacency.html

to PETSC_TRUE, PETSC_FALSE, but you are probably doing everything
matrix-free if you are using DG.
The above is optimal for FV, but not for DG because you communicate more
than you absolutely have to.

A more complicated, but optimal, thing to do would be to assign interior
dofs to the cell, and two sets of dofs
to each face, one for each cell. Then you only communicate the face dofs.
Its just more bookkeeping for you,
but it will work in parallel just fine.

I don't think you need extra vertices, or coordinates, and for output I
recommend using DMPlexProject() to get
the solution in some space that can be plotted like P1, or anything else
supported by your visualization.

  Thanks,

     Matt

>
> >        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/>
>


-- 
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/>
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