Dear Hamed,

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). 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. So, in my opinion, it would 
make sense to use this function in the way that you've described to 
generate your mesh prior to further refinement, be that via global or local 
refinement. 

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>
.

I hope that this help.

Regards,
Jean-Paul


On Saturday, May 13, 2017 at 1:00:08 AM UTC+2, Hamed Babaei wrote:
>
> Hello,
>
> I want to apply periodic boundary condition on a 3D thin square plate with 
> one element in the thickness direction. I have already used the following 
> for meshing
>
> std::vector< unsigned int > repetitions(dim, 100);
>     if (dim == 3)
>     repetitions[dim-1] = 1;
> GridGenerator::subdivided_hyper_rectangle(triangulation,
>                                                                repetitions,
>                                                               
>  /*bottom_left*/ Point<dim>(0.0, 0.0, -0.5),
>                                                               /* 
> top_right*/ Point<dim>(20.0, 20.0, 0.5),
>                       true); 
>
> However, when applying periodic condition, mesh refinement should be 
> applied after doing "triangulation.add_periodicity(periodicity_vector)".
> So I have to first just use "hyper_rectangle" without any repetition 
> argument to create the geometry, then after I added periodicity to the 
> faces, mesh refinement can be applied.
> Yet, I am wondering which function can apply different refinement for 
> different directions, since " triangulation.refine_global ()" do the same 
> for all directions.
>
> Thanks and regards,
> Hamed
>

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