[petsc-users] Periodic boundary conditions in DMPlex

Fri Oct 15 15:30:12 CDT 2021

On Fri, Oct 15, 2021 at 10:16 AM Pierre Seize <pierre.seize at onera.fr> wrote:

> I read everything again, I think I did not understand you at first. The
> first solution is to modify the DAG, so that the rightmost cell is linked
> to the leftmost face, right ? To do that, do I have to manually edit the
> DAG (the mesh is read from a file) ?
>
Yes, the DAG would be modified if you want it for some particular mesh that
we cannot read automatically. For example, we can read periodic GMsh
meshes.

> If so, the mesh connectivity is like the one of a torus, then how does it
> work with the cells/faces coordinates ?
>
You let the coordinate field be in a DG space, so that it can have jumps.

> Now I think the second method may be more straightforward. What's the idea
> ? Get the mapping with DMGetLocalToGlobalMapping, then create the mapping
> corresponding to the periodicity with ISLocalToGlobalMappingCreate, and
> finally ISLocalToGlobalMappingConcatenate ? I'm not sure this is the way,
> and I did not find something like DMSetLocalToGlobalMapping to restore the
> modified mapping.
>
It is more complicated. We make the LocalToGlobalMap by looking at the
PetscSection (essentially if gives function space information)  and
deciding which unknowns are removed from the global space.
You would need to decide that unknowns constrained by periodicity are not
present in the global space. Actually, this is not hard. You just mark them
as constrained in the PetscSection, and all the layout
functions will function correctly. However, then the LocalToGlobalMap will
not be exactly right because the constrained unknowns will not be filled in
(just like Dirichlet conditions). You would augment the
map so that it fills those in by looking up their periodic counterparts.
Jed has argued for this type of periodicity.

To me, the first kind is much more straightforward, but maybe this is
because I find the topology code more clear.

  Thanks,

      Matt

> Pierre
>
> On 15/10/21 15:33, Pierre Seize wrote:
>
> When I first tried to handle the periodicity, I found the
> DMPlexCreateBoxMesh function (I cannot find the cylinder one).
>
> From reading the sources, I understand that we do some work either in
> DMPlexCreateCubeMesh_Internal or with DMSetPeriodicity.
>
> I tried to use DMSetPeriodicity before, for example with a 2x2 box on
> length 10. I did something like:
> const PetscReal maxCell[] = {2, 2};
> const PetscReal L[] = {10, 10};
> const DMBoundaryType bd[] = {DM_BOUNDARY_PERIODIC, DM_BOUNDARY_PERIODIC};
> DMSetPeriodicity(dm, PETSC_TRUE, maxCell, L, bd);
> // or:
> DMSetPeriodicity(dm, PETSC_TRUE, NULL, L, bd);
>
> but it did not work:
> VecSet(X, 1);
> DMGetLocalVector(dm, &locX);
> VecZeroEntries(locX);
> DMGlobalToLocalBegin(dm, X, INSERT_VALUES, locX);
> DMGlobalToLocalEnd(dm, X, INSERT_VALUES, locX);
> VecView(locX, PETSC_VIEWER_STDOUT_WORLD);
>
> but the ghost cells values are all 0, only the real cells are 1. So I
> guess DMSetPeriodicity alone is not sufficient to handle the periodicity.
> Is there a way to do what I want ? That is set up my DMPlex in a way that
> DMGlobalToLocalBegin/DMGlobalToLocalEnd do exchange values between procs
> AND exchange the periodic values?
>
>
> Thanks for the help
>
>
> Pierre
>
> On 15/10/21 14:03, Matthew Knepley wrote:
>
> On Fri, Oct 15, 2021 at 7:31 AM Pierre Seize <pierre.seize at onera.fr>
> wrote:
>
>> It makes sense, thank you. In fact, both ways seems better than my way.
>> The first one looks the most straightforward. Unfortunately I do not know
>> how to implement either of them. Could you please direct me to the
>> corresponding PETSc functions ?
>>
> The first way is implemented for example in DMPlexCreateBoxMesh() and
> DMPlexCreateCylinderMesh(). The second is not implemented since
> there did not seem to be a general way to do it. I would help if you
> wanted to try coding it up.
>
>   Thanks,
>
>     Matt
>
>> Pierre
>>
>> On 15/10/21 13:25, Matthew Knepley wrote:
>>
>> On Fri, Oct 15, 2021 at 7:08 AM Pierre Seize <pierre.seize at onera.fr>
>> wrote:
>>
>>> Hi,
>>>
>>> I'm writing a code using PETSc to solve NS equations with FV on an
>>> unstructured mesh. Therefore I use DMPlex.
>>>
>>> Regarding periodicity, I manage to implement it this way:
>>>
>>>    - for each couple of boundaries that is linked with periodicity, I
>>> create a buffer vector with an ISLocalToGlobalMapping
>>>
>>>    - then, when I need to fill the ghost cells corresponding to the
>>> periodicity, the i "true" cell of the local vector fills the buffer
>>> vector on location i with VecSetValuesBlockedLocal, then
>>> VecAssemblyBegin/VecAssemblyEnd ensure each value is send to the correct
>>> location thanks to the mapping, then the i "ghost" cell of the local
>>> vector reads the vector on location i to get it's value.
>>>
>>>
>>> It works, but it seems to me there is a better way, with maybe PetscSF,
>>> VecScatter, or something I don't know yet. Does anyone have any advice ?
>>>
>>
>> There are at least two other ways to handle this. First, the method that
>> is advocated in
>> Plex is to actually make a periodic geometry, meaning connect the cells
>> that are meant
>> to be connected. Then, if you partition with overlap = 1,
>> PetscGlobalToLocal() will fill in
>> these cell values automatically.
>>
>> Second, you could use a non-periodic geometry, but alter the
>> LocalToGlobal map such
>> that the cells gets filled in anyway. Many codes use this scheme and it
>> is straightforward
>> with Plex just by augmenting the map it makes automatically.
>>
>> Does this make sense?
>>
>>   Thanks,
>>
>>      Matt
>>
>>
>>> Pierre Seize
>>>
>> --
>> 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/%7Eknepley/>
>>
>>
>>
>
> --
> 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/%7Eknepley/>
>
>
>
>

-- 
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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