[petsc-dev] DMPlex "chart" term

[Matthew Knepley]

On Wed, Oct 11, 2017 at 10:55 AM, Patrick Sanan <patrick.sanan at gmail.com>
wrote:

> On Wed, Oct 11, 2017 at 10:58 AM, Matthew Knepley <knepley at gmail.com>
> wrote:
>
>> On Wed, Oct 11, 2017 at 4:54 AM, Patrick Sanan <patrick.sanan at gmail.com>
>> wrote:
>>
>>> Another terminology question to help with the docs.
>>>
>>> What's the origin of the term "chart" in DMPlex? I'm only previously
>>> familiar with the term in the context of manifolds (where chart =
>>> homeomorphism from an open set in the manifold to an open set in R^n).
>>>
>>
>> That is what it is supposed to be. A chart is coordinates on a patch of
>> the manifold. We intend the same thing here in that you can
>> locally refer to points with a given name, but they may have a different
>> name on another chart (process). The names are matched up using the PetscSF.
>>
>
> So do you mean that you think of the DMPlex (thought of just as a set of
> points) as some kind of a "manifold over the integers"
>

I don't think it helps to say "integers" since we do not use any arithmetic
property, but we do have a graph representing a manifold, where
the chart should really be the full topology, but we use [s, e) for a
shorthand, and the transition map is indeed the SF since that allows us
to piece together the topologies to form a global topology.

  Thanks,

     Matt


> and consider an "atlas" with one patch per proc, with the SF defining the
> "transition maps"?
>
>
>>
>>> In terms of the use in DMPlex, is there anything wrong with thinking of
>>> "chart" as a shorter way to say "interval of integers, closed on the left
>>> and open on the right, e.g.  [pStart,pEnd)"?
>>>
>>
>> No, since we depend on continuity of point names almost everywhere.
>>
>>   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
>>
>> https://www.cse.buffalo.edu/~knepley/ <http://www.caam.rice.edu/~mk51/>
>>
>
>


-- 
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.caam.rice.edu/~mk51/>
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