Bruno,

thanks a lot for the clarification. Now that I read the docu again, it also 
seems clear to me that one has to construct the matrix oneself. 

The transfer representation contains the information on how to map a coarse 
grid dof to the fine grid. This can be transformed to a matrix of size 
(dof_handler_fine.n_dofs(), dof_handler_coarse.n_dofs()). Directly applying 
this matrix to a vector leaves a lot of zero entries (i.e. those vector 
entries that don't have a dof correspondence on the coarse grid). See the 
attached image. 

So we still need to interpolate between the coarse values in the fine 
space. The only interpolation function that I found that uses a 
transformation matrix was this one 
https://dealii.org/8.5.0/doxygen/deal.II/namespaceVectorTools.html#a5e3af70a47cedfaf361cf5c621e94e3d.
When looking into the implementation of this function, the interpolation 
function expects a FullMatrix of size 
(dof_handler_fine.get_fe().dofs_per_cell, 
dof_handler_coarse.get_fe().dofs_per_cell), so it has to map the cell data 
of individual cells to each other. I don't think that the transfer 
representation matrix can provide this information.

Do you know how to create the matrix needed by the interpolate function 
using the data of the transfer representation? If not, is there another way 
to interpolate using a transfer matrix? Thanks a lot for your help.

Best,
Ina

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