[dune-pdelab] dim < dimWorld ?

[Bernd Flemisch]

Dear DUNE-PDELab,

some people here including me are wondering what are your current 
thoughts on performing calculations with dim < dimWorld? Has someone 
already used PDELab for this or plans to do so?

Looking, e.g., at localoperator/convectiondiffusion.hh, line 310ff, I find

const Dune::FieldMatrix<DF,dimw,dim> jac = 
eg.geometry().jacobianInverseTransposed(it->position());
std::vector<Dune::FieldVector<RF,dim> > gradphi(lfsu.size());
for (size_type i=0; i<lfsu.size(); i++)
{
   gradphi[i] = 0.0;
   jac.umv(js[i][0],gradphi[i]);
}

This will not work for dimw != dim, since jac is dimWorld x dim, and 
should map the dim-vector js[i][0] to a dimWorld-vector. However gradphi 
is a dim-vector.

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.

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?

Thank you for your thoughts. Kind regards
Bernd

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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
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