dolfin team mailing list archive

["Alessio Quaglino" <alessio@xxxxxx>]

> 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.

What about two meshes where one is the refined version of the other, i.e.
they share the same hierarchy? It might be easy to "colour" patches of
triangles in the finer mesh corresponding to one triangle of the coarser.
I'm not aware of the internal algorithms of dolfin though, and hence I
don't know where to start in doing this.

Alessio


>> 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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