dolfin team mailing list archive

["Alessio Quaglino" <alessio@xxxxxx>]

>> 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

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?

Alessio