[petsc-dev] indexing for periodic BC

[Matthew Knepley]

On Sun, Jun 19, 2011 at 1:38 PM, Jed Brown <jed at 59a2.org> wrote:

> On Fri, Jun 17, 2011 at 23:00, Barry Smith <bsmith at mcs.anl.gov> wrote:
>
>>  It is possible that list of elements is not correct for periodic boundary
>> conditions; I've never used it. I'm forwarding this to petsc-dev so Matt can
>> check it and see if the elements make sense and what indices they routine
>> (are the local, global? I don't know) if they are local then maybe you don't
>> need to the MatSetValuesStencil() and just call MatSetValuesLocal().
>
>
> The function returns local indices, so you would use MatSetValuesLocal(). I
> put a link to these in the documentation.
>
> But the implementation is not correct for periodic domains. It should not
> be a great deal of work to implement. You would just need to teach that
> function about the "wrap-around" elements. But this is actually not trivial
> for a mapped grid. In no case can you just use the coordinates that were set
> on the DMDA, you have to extrapolate. But it's unclear how to extrapolate
> for a non-uniform mesh in order to make the periodic problem consistent. I
> don't think this is easy to rectify without changing the API for managing
> coordinates, but you can certainly make it work for regular Cartesian grids.
>
> By the way, I think the whole premise of DMDAGetElements() is flawed. Shape
> functions are not provided so the user has to implement those themselves and
> manage consistency. The actual logic inside DMDAGetElements() is really
> small compared to defining quadratures and basis functions, so it's no
> particular effort for the user to manage it on their own. Additionally,
> managing it on their own will perform somewhat better (no intermediate
> indexing structures) and gives more flexibility in boundary conditions.
>
> It might not be a bad idea to offer an easy-to-use, first order only,
> structured grid FEM API, but this ain't it.
>

Yes, I do not disagree that DMDAGetElements() is flawed. We just do not have
anything better right now.

   Matt

-- 
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
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