dolfin team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

On Fri, Nov 23, 2007 at 02:17:14PM +0100, Alessio Quaglino wrote:
> >> On Tue, May 15, 2007 at 06:42:18PM +0200, Johan Jansson wrote:
> >>> > Johan H., Johan J.,
> >>> >
> >>> > Could you add a demo for the projection of a function onto different
> >>> > meshes? I'd really like to see how it works.
> >>> >
> >>> > Garth
> >>>
> >>> Hi!
> >>>
> >>> There is such a demo in:
> >>>
> >>> src/demo/fem/nonmatching
> >>
> >> Does not exist.
> >>
> >>> also in:
> >>>
> >>> src/demo/pydolfin/projection/verification
> >>> src/demo/pydolfin/projection/nonmatching-continuous
> >>> src/demo/pydolfin/projection/nonmatching-discontinuous
> >>
> >> None of these work.
> >>
> >>> A mesh refinement/coarsening demo exists in:
> >>>
> >>> src/demo/mesh
> >>
> >> Moved to src/demo/mesh/refinement and I don't think it works, but it
> >> does do a lot of printing and says "mesh not ok" :-)
> >>
> >>> Note that I haven't tested these demos with the dolfin repository
> >>> version
> >>> for a while, I'll try to do that in the near future. Also note that
> >>> there
> >>> is still a major (but quite simple) optimization left for the
> >>> projection
> >>> -
> >>> to exploit that we know which cell of the target mesh we are on when
> >>> evaluating functions on the source mesh (we only have to search through
> >>> the intersecting cells and not the whole mesh). So currently the time
> >>> complexity is not very good, but the implementation is robust.
> >>>
> >>>   Johan
> >>
> >> Sounds good.
> >>
> >> /Anders
> >
> > Was this projection between different meshes implemented? I can't find
> > anything about it inside the documentation.
> >
> > Alessio
> 
> I'm trying to think about how to implement this in the case of two meshes,
> one being the refined version of the other. Let us call u and U the
> function we want to project on the coarse (N dof) and fine (M dof) mesh
> respectively, defined as:
> 
> u = \sum_i u_i phi_i
> U = \sum_i U_i psi_i
> 
> where phi_i and psi_i are the test functions on the coarser and finer mesh
> respectively. We want thus to satisfy the following:
> 
> \int (u - U) phi = 0
> 
> which becomes:
> 
> \sum_i (u_i phi_i phi_j) = \sum_i (U_i psi_i phi_j) for j = 1:N

Yes, the key difficulty is integrating a product of two functions
defined on different meshes.

> we now want to compute those sums onto the coarser mesh. However, in order
> to do this, we have to evaluate phi (basis function of the coarser mesh)
> on the finer mesh since the sum goes i=1:M with M>N. Can FEniCS do that
> automatically?

No, not yet. There was some work done on this a while ago (at KTH) but
I don't know what happened to it.

/Anders


> Alessio
> 
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