[petsc-users] explanations on DM_BOUNDARY_PERIODIC

[neok m4700]

Hello Barry,

Thank you for answering.

I quote the DMDA webpage:
"The vectors can be thought of as either cell centered or vertex centered
on the mesh. But some variables cannot be cell centered and others vertex
centered."

So If I use this, then when creating the DMDA the overall size will be the
number of nodes, with nodal coordinates, and by setting DMDA_Q0 interp
together with DM_BOUNDARY_PERIODIC I should be able to recover the solution
at cell centers ?

I that possible in PETSc or should I stick to the nodal representation of
my problem ?

thanks.

2017-04-27 20:03 GMT+02:00 Barry Smith <bsmith at mcs.anl.gov>:

>
> > On Apr 27, 2017, at 12:43 PM, neok m4700 <neok.m4700 at gmail.com> wrote:
> >
> > Hi Matthew,
> >
> > Thank you for the clarification, however, it is unclear why there is an
> additional unknown in the case of periodic bcs.
> >
> > Please see attached to this email what I'd like to achieve, the number
> of unknowns does not change when switching to the periodic case for e.g. a
> laplace operator.
>
>    So here you are thinking in terms of cell-centered discretizations. You
> are correct in that case that the number of "unknowns" is the same for both
> Dirichlet or periodic boundary conditions.
>
>    DMDA was originally written in support of vertex centered coordinates,
> then this was extended somewhat with DMDASetInterpolationType() where
> DMDA_Q1 represents piecewise linear vertex centered while DMDA_Q0
> represents piecewise constatant cell-centered.
>
>     If you look at the source code for DMDASetUniformCoordinates() it is
> written in the context of vertex centered where the coordinates are stored
> for each vertex
>
>    if (bx == DM_BOUNDARY_PERIODIC) hx = (xmax-xmin)/M;
>     else hx = (xmax-xmin)/(M-1);
>     ierr = VecGetArray(xcoor,&coors);CHKERRQ(ierr);
>     for (i=0; i<isize; i++) {
>       coors[i] = xmin + hx*(i+istart);
>     }
>
> Note that in the periodic case say domain [0,1) vertex centered with 3
> grid points (in the global problem) the coordinates for the vertices are 0,
> 1/3, 2/3 If you are using cell-centered and have 3 cells, the coordinates
> of the vertices are again 0, 1/3, 2/3
>
> Note that in the cell centered case we are storing in each location of the
> vector the coordinates of a vertex, not the coordinates of the cell center
> so it is a likely "wonky".
>
>    There is no contradiction between what you are saying and what we are
> saying.
>
>    Barry
>
> >
> > And in the case of dirichlet or neumann bcs, the extremum cell add
> information to the RHS, they do not appear in the matrix formulation.
> >
> > Hope I was clear enough,
> > thanks
> >
> >
> > 2017-04-27 16:15 GMT+02:00 Matthew Knepley <knepley at gmail.com>:
> > On Thu, Apr 27, 2017 at 3:46 AM, neok m4700 <neok.m4700 at gmail.com>
> wrote:
> > Hi,
> >
> > I am trying to change my problem to using periodic boundary conditions.
> >
> > However, when I use DMDASetUniformCoordinates on the DA, the spacing
> changes.
> >
> > This is due to an additional point e.g. in dm/impls/da/gr1.c
> >
> > else if (dim == 2) {
> >     if (bx == DM_BOUNDARY_PERIODIC) hx = (xmax-xmin)/(M);
> >     else hx = (xmax-xmin)/(M-1);
> >     if (by == DM_BOUNDARY_PERIODIC) hy = (ymax-ymin)/(N);
> >     else hy = (ymax-ymin)/(N-1);
> >
> > I don't understand the logic here, since xmin an xmax refer to the
> physical domain, how does changing to a periodic BC change the
> discretization ?
> >
> > Could someone clarify or point to a reference ?
> >
> > Just do a 1D example with 3 vertices. With a normal domain, you have 2
> cells
> >
> >   1-----2-----3
> >
> > so each cell is 1/2 of the domain. In a periodic domain, the last vertex
> is connected to the first, so we have 3 cells
> >
> >   1-----2-----3-----1
> >
> > and each is 1/3 of the domain.
> >
> >    Matt
> >
> > Thanks
> >
> >
> >
> > --
> > 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
> >
> > <1D.pdf>
>
>
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