[Dune] dim < dimworld ?

Oliver Sander sander at mi.fu-berlin.de
Wed Aug 29 10:01:14 CEST 2007

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.


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  *
* Arnimallee 6                 ** -------------------------------------*
* 14195 Berlin, Germany        ** Member of MATHEON (www.matheon.de)   *

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