[Dune] Understanding LocalGeometry

[Carsten Gräser]

Hi,

Am 13.01.2015 um 10:25 schrieb Aleksejs Fomins:
> Dear Dune,
> 
> I am trying to understand what is a LocalGeometry object that is
> returned by, for example, intersection.geometryInInside(). As in, what
> is the difference between Geometry and LocalGeometry classes?
in general LocalGeometries describe embeddings of local coordinate
system, e.g., son->father, intersection->element.

> If I were to guess, I'd say that LocalGeometry is the geometry class
> implementation for a reference element coordinates, for example
> {(0,0,0) (1,0,0) (0,1,0) (0,0,1) } for a tetrahedron.
I don't complete understand this, but I guess it's not true,
because this would be a full dimensional simplex. Instead of
this geometryInInside is the geometry that embeds local
(d-1)-dimensional coordinates of the intersection into the local
d-dimensional coordinate system of the element.

So its more like {(0,0,0), (.5,0,0), (0,.5,0)} for a triangular
face of a tetrahedron on nonconforming intersection with a first
order hanging node.

> Now I could in principle define
> LocalGeometry = CachedCurvilinearGeometry<interp_order = 1>, but is
> this what is expected? I mean, the machinery of this class is way too
> heavy and unnecessary for the purposes of a simple linear geometry.
Since the LocalGeometry does only carry ('topological') information on
local embeddings, it is agnostic wrt the element geometry.
Hence I guess that you could simply forward the one from the
host grid.

Best,
Carsten

> How is this class usually defined in other grid managers. Is there
> some standard ReferenceGeometry or sth that can be used for this purpose?
> 
> Cheers,
> Aleksejs

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