[Dune] Understanding LocalGeometry

[Aleksejs Fomins]

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Dear Carsten,

Thank you for your reply. I get it now :)

Aleksejs


On 13/01/15 11:26, Carsten Gräser wrote:
> 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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