[dune-pdelab] dim < dimWorld ?

[Bernd Flemisch]

Hey Christian and Dan,

thank you for your fast answers. I acknowledge the fact 
that the gradient is a dimWorld object and that it can be 
represented in a dimWorld coordinate system. From that 
perspective, I can understand that 
jacobianInverseTransposed maps to dimWorld.

Nevertheless, I would say that the best way of describing 
the problem to be assembled is by surface quantities like 
differential operators div_s, grad_s and diffusion tensors 
D_s. Of course, they can be represented in a dimWorld 
coordinate system. But that means that I have to blow up 
everything. For example for dim=1, I would have a scalar 
tangential diffusion coefficient and I would have to blow 
that up to a dimWorld x dimWorld tensor. Isn't that 
inefficient?

But ok, I guess my preferred way to do it is to project 
the dimWorld-representation of the gradient to the surface 
and a dim-representation. Then one can apply 
dim-representations of e.g. tangential diffusion tensors.

Kind regards
Bernd

On Wed, 9 May 2012 18:19:04 +0200
  Christian Engwer <christian.engwer at uni-muenster.de> 
wrote:
> Hi Bernd,
> 
>> One could fix this by declaring gradphi as a 
>>dimWorld-vector, but I
>> don't think that this is what we want to do. We want to 
>>solve an
>> equation like
>> div_s D_s grad_s u_s = q_s
>> where all _s are surface quantities. The vectors and 
>>tensors have a
>> dimWorld coordinate representation, but I think that one 
>>would want
>> to use the dim representations.
> 
> on the contrary, if you look into the sfem stuff, you 
>consider a
> problem in dimW, but assemble on the surface.
> 
>> So either jacobianInverseTransposed should map to a 
>>dim-coordinate
>> vector, or one should have a method for projecting
>> dimWorld-representations to dim-representations. What do 
>>you think?
> 
> you are mapping to global coordinates and these are 
>dimW, so the
> jacobian has to map to dimW aswell.
> 
> I agree that some (or most) operators will not work for 
>surface
> problems, but the necessary changes are simply to use 
>the appropriate
> vector sizes.
> 
> Christian
> 

___________________________________________________________

Bernd Flemisch                     phone: +49 711 685 
69162
IWS, Universitaet Stuttgart          fax: +49 711 685 
67020
Pfaffenwaldring 61        email: 
bernd at iws.uni-stuttgart.de
D-70569 Stuttgart        url: 
www.hydrosys.uni-stuttgart.de
___________________________________________________________