In my project I already managed to replace the system_matrix in the 
solve()-call by a custom LinearOperator, but still I had to retain the 
matrix itself (for the preconditioner, for example). Thus I am now trying 
to use the MatrixFree-framework for that.
Thus, some questions arose:

   - When using the LinearOperator, the function vmult() is used when 
   solving the system with a GMRES-solver (or similar). Does the same hold up 
   for the MatrixFree-framework?
   - If the above is correct: In each GMRES-iteration I have to calculate 
   the residual of my equation, once for the current solution and once for the 
   current solution + a small step. At the moment I calculate the residual by 
   summing the terms into my residual vector, and then distributing the values 
   while setting the boundary condition to 0. If I understand it correctly, 
   that happens as soon as I call phi.distribute_local_to_global(dst), with 
   phi a FEEvaluation-element. This means that I first have to assemble the 
   residual vector, then distribute it, and then can use the vmult-function. 
   Is that correct, or do I have to use another approach?

Thanks!

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