Dear Jean-Paul,

Thank you for your prompt help.

Although I don't really understand your specific question, I am guessing 
> that you were wondering if its possible to use the "repetitions" parameter 
> to bias the initial mesh gradation before adding periodicity (since the 
> periodic face pairs must be chosen on the on the coarsest mesh).
>
 
Yes, you are right. In fact, I do not want to refine the mesh but generate 
the initial mesh in away that mesh discritisation is done after adding 
periodicity.
 

> To the best of my knowledge, GridGenerator::subdivided_hyper_rectangle 
> generates a coarsest level mesh (i.e. all cells have level = 0) with the 
> given discretisation in each coordinate direction. 
>

It seems that GridGenerator::subdivided_hyper_rectangle needs repetition 
argument and complete mesh generation in one step. so cells have level=1 .
 

> You could also consider using anisotropic refinement (see step-30 
> <https://www.dealii.org/8.5.0/doxygen/deal.II/step_30.html>), but this 
> feature is not so commonly used (as far as I can tell) and it is not 
> supported by all Triangulations 
> <https://www.dealii.org/8.5.0/doxygen/deal.II/classparallel_1_1distributed_1_1Triangulation.html>
> .
>

Since my code is parallel, I am wondering what is the alternative for me.


Thanks and regards,
Hamed
 

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