[dune-pdelab] dim < dimWorld ?

[Bernd Flemisch]

Hey Christian,

> I think the beauty of sfem is that you can write it without really
> noticing that you compute something on a surface just by using the
> correct jabians etc.
That might be beautiful for a dimWorld-god with his dimWorld coordinate 
system. I thought that the beauty of a dim < dimWorld approach would 
come from the fact that one most often can be a dim-beetle crawling  
around on the dim-surface with a dim coordinate system living in happy 
ignorance and not having to care about the dimWorld gods.

> This is also the only way, I see, to ensure that
> you can run the same operator on both grids.
This is of course a strong point. Would PDELab in principle be receptive 
for patches trying to make some of the local operators consistent for 
dim < dimWorld?

Kind regards
Bernd

>
> Christian
>
> On Wed, May 09, 2012 at 07:19:48PM +0200, Bernd Flemisch wrote:
>> 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
>> ___________________________________________________________
>>
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-- 
_____________________________________________________________________

Bernd Flemisch                               phone: +49 711 685 69162
IWS, Universität Stuttgart                   fax:   +49 711 685 60430
Pfaffenwaldring 61                  email: bernd at iws.uni-stuttgart.de
D-70569 Stuttgart                  url: www.hydrosys.uni-stuttgart.de
_____________________________________________________________________