[dune-pdelab] dim < dimWorld ?

[Christian Engwer]

Hi Bernd,

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. This is also the only way, I see, to ensure that
you can run the same operator on both grids.

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
> ___________________________________________________________
> 
> _______________________________________________
> dune-pdelab mailing list
> dune-pdelab at dune-project.org
> http://lists.dune-project.org/mailman/listinfo/dune-pdelab
>