[Dune] parallel DUNE grid for implementing a spherical shell (UGGrid)

[Eike Mueller]

Dear dune-list,

can anyone help me with the following question about UG grid:

I want to create a parallel grid representing a spherical shell, with one level in the radial direction only. I have tried this with UGGrid and the GridFactory class. To create a cubed sphere grid, I created 2x8 vertices, describing two nested cubes with factory.insertVertex(). I then create the corresponding 12 elements with factory.insertElement() and describe the projection onto the sphere by using factory.insertBoundarySegment() for each of the 2x12 faces (12 inner faces and 12 outer faces). Before doing any refinement I get the macro grid in the attached file cubed sphere_macro.vtu.
If I then call globalRefine(), the grid gets refined in all three dimensions and I end up with the attached refined grid cubed sphere_refined.vtu.

Now my two questions are as follows:

(1) How can I ensure that the grid is not refined in the radial direction, i.e. I always only end up with one layer of cells in the radial direction? I guess I have to run over the grid and mark cells for refinement, but is this documented anywhere in more detail?
(2) The parallel load balancing does not seem to work. If I run on 24 processes and I call globalRefine(), followed by loadBalance(), some processes end up with no part of the grid. I have checked that I use the parallel version of UG grid.

I attach the code I used to generate the grid, as well as the .vtu files mentioned above.

Thanks a lot for any help,

Eike

PS: Alternatively, I would also be equaully happy if I can create a PARALLEL 2d surface grid for the surface of the sphere (again, either cubed sphere or a icosahedral grid). However, as far as I can see it, there is no parallel implementation for this, we've tried 2d ALUGRID, parallelised with the metagrid approach, but this does not scale beyond a few hundred processors as the entire grid is stored on each processor and my code runs out of memory.

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