[Dune] ID for an interface

[Markus Blatt]

Hey,

we should  merge your perfect and nice answer to the DUNE-FAQ,
shouldn't we?

Markus

On Mon, May 16, 2011 at 12:04:00PM +0200, Jö Fahlke wrote:
> Am Mon, 16. May 2011, 11:27:09 +0200 schrieb Benjamin Faigle:
> > if i understood it right, the method
> > 	grid.localIdSet().id(const EntityType &e)
> > should return a unique ID for every sort of entities, be it
> > elements, vertices or intersections. It works out pretty well with
> > elements, as shown for example in the Dune Grid Howto
> > 	IdType idf = idset.id (* ep );
> > 
> > However, if I try the same with an *intersection, I get the error message:
> > ...dune-grid/dune/grid/common/indexidset.hh:394:43: error:
> > ‘codimension’ is not a member of ‘Dune::IntersectionIterator<const
> > Dune::UGGrid<2>, Dune::UGGridLeafIntersectionIterator,
> > Dune::UGGridLeafIntersection>’
> > 
> > I am using dune 2.0.
> > I am sorry if it is just an incredibly silly question, and many
> > thanks for your help,
> 
> Only entities have ids.  Intersections are not entities!
> 
> All grids have entities of codimension dim (vertices) and codimension 0
> (elements), and all have intersections.  Some grids have entities of other
> codimensions as well.  Even if a grid has entities of codimension 1, these are
> not the same as entities.  Most obvious differences:
> 
>  * Intersections know the neighbouring cells, codim 1 entities don't.
> 
>  * Intersections have an orientation, codim 1 entities don't.
> 
>  * Codim 1 entities have indices and ids and can be used to obtain array
>    indices from a mapper (even if the grid does not support codim 1 entity
>    objects!)  For intersections, indices, id's and maps are not provided by
>    core Dune, though it is possibly to build such things yourself.
> 
>  * In non-conforming grids you may have the following situation:
> 
>      +-------+---+---+
>      |       | b | d |
>      |   a   +---+---+
>      |       | c | e |
>      +-------+---+---+
> 
>    Elements b, c, d and e all have four codim 1 subentities and four
>    corresponding intersections.  Element a also has four codim 1 subentities,
>    but it has five intersections.  The codim 1 entity to the right of b is the
>    same as the codim 1 entity to the left of d.  You have three codim 1
>    entities to the right of a however: on covering the whole of a's right
>    border, and two smaller one each covering the upper and the lower half of
>    a's border, respectively.
> 
> If you know you have a conforming grid, you have a correspondance between
> intersections and codim 1 entities (ignoring the orientation of the
> intersections).  In that case you can usually get away by using the id of the
> corresponding codim 1 entity as the id of the intersection (even if the grid
> does not support codim 1 entities as independent objects.  Use
> 
>   grid.globalIdSet().subId(e, i.indexInInside(), 1);
> 
> where i is the intersection and e is the codim 0 entity i was obtained from.
> If you don't have e readily available, you can use
> 
>   grid.globalIdSet().subId(*i.inside(), i.indexInInside(), 1);
> 
> instead.
> 
> Bye,
> Jö.
> 



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-- 
Markus Blatt, Interdisciplinary Center for Scientific Computing,
University Heidelberg, Im Neuenheimer Feld 368, D-69120 Heidelberg

'Mathematics knows no races or geographic boundaries; for
mathematics, the cultural world is one country' - David Hilbert