[Dune] dim < dimworld ?

[Oliver Sander]

Hi Bernd!
Sounds like interesting stuff.  Maybe the following ideas can help  you.

It is very unlikely that SGrid or YaspGrid will ever support affine or
more general embeddings in higher-dimensional spaces.  Such a
feature would go to the detriment of their normal performance,
which is more important.

1d-in-2d:  Peter Bastian's group has a grid manager for general
1d grids in an n-d world.  The last time I asked they were pretty
reluctant to give it away, though.  Please ask them directly for
details.  Your second-best option is to use a 1d-1d grid and write
a special assembler with an external geometry.

2d-in-3d: Our group is working on multigrid methods for various PDEs
on 2d-manifolds in 3d.  Therefore we are also very interested in such a
grid manager.  Currently we use special-purpose assemblers which
operate on the boundary of UGGrid<3> objects.  That gives you mixed
2d grids in 3d with adaptive refinement and arbitrary parametrizations.
On the other hand you have to hand-code your assembler and use
lots of memory.

The demand for a 2d-in-3d grid seems to grow.  Maybe we should start
thinking about how to implement one.

--
Oliver

Bernd Flemisch schrieb:
>>> Dear Dune developers,
>>>
>>> we plan to have dim < dimworld. As far as I can see, this is not yet
>>> supported (in SGrid partially, but, e.g., the dimworld normals are
>>> wrong). Do you plan to support it, and, if yes, when?
>>>
>>> Thanks. Best wishes
>>> Bernd
>>>
>>>   
>>>       
>> Hi Bernd!
>> Yes, we certainly intend to support this.  However, there has not been
>> much demand for it so far.  It would be nice to have, e.g., a grid
>> manager for 2d-in-3d simplicial surfaces, but afaik there's none in
>> sight.  What exactly do you need?
>>
>> -- 
>> Oliver
>>
>>     
> Hi Oliver,
>
> thanks for the quick response. The grid manager for 2d-in-3d simplicial
> surfaces is exactly what I would need in the long run.
> Talking applications, we have two in mind where it would be nice to have
> dim < dimworld: the first one is pipe flow embedded in a porous medium
> yielding a 1d grid in a 2d/3d world. The second one is flow in fractures
> embedded in a porous medium yielding a 1d grid in a 2d world or a 2d
> grid in a 3d world.
> For 1d in 2d/3d, a first step would be to have an SGrid for a straight
> line. Up to now, some features are already working if this line is of
> the form (x(t), y(t)) = (a + t, a + t). If you could specify arbitrary
> start and end points, that would already be enough to keep us busy for
> quite a while.
> After that, it would be nice to be able to deal with curved lines. And
> finally, the grid manager for 2d-in-3d simplicial surfaces...
>
> Best wishes
> Bernd
>
>
>   


-- 
************************************************************************
* Oliver Sander                ** email: sander at mi.fu-berlin.de        *
* Freie Universität Berlin     ** phone: + 49 (30) 838 75217           *
* Institut für Mathematik II   ** URL  : page.mi.fu-berlin.de/~sander  *
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