Rajat,

I am using the GridGenerator::hyper_rectangle function to create a 
> rectangular grid with 1000 X 500 X 1 (0.5 million) elements.
>
> My question is: - since the coarsest mesh contains 0.5 million elements, 
> does that mean all the processors have 0.5 million elements?
> (I think the answer is yes, I read that the deal.ii (p4est) stores the 
> coarsest mesh on all processors.)
>
Yes, that is true. 

I need a mesh (overall) which should be rectangular and should have 1000 X 
> 500 X 1 elements. Note: It should only have 1 element in the z-direction.
> Is there any way such that I can have this mesh by not replicating the 
> whole mesh on all processors as it takes a lot of memory. I thought of 
> making a 2D mesh and then refining it and then extruding it using 
> extrude::triangulation, but extrude triangulation does not work on refined 
> meshes.
>
As you already said, we (currently) require to store the same coarse mesh 
on all processes and only isotropic refinement is allowed. This means that 
you can get 1 element in z-direction if you don't refine. There is some 
work [1] on a Triangulation that allows you to specify the distribution of 
cells across processes yourself without the need of a common coarse mesh.

Best,
Daniel

[1] https://github.com/dealii/dealii/pull/3956

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