Wolfgang,

Thanks for your response.  That makes a lot of sense.  I suppose they are many 
competing requirements in defining an "optimal" partitioning, particularly as 
you go to large numbers of processors.  

> To make this less likely, deal.II sorts the coarse mesh cells by a 
> Cuthill-McKee algorithm, which is why you see the concentric shells: Cuthill-
> Mckee orders the cells one shell at a time.
> 
> I think this algorithm makes things a bit better, but it's certainly still 
> not 
> good. I think it's also not bad once you have many more processors than 
> coarse 
> mesh cells -- or, alternatively, if you have many more coarse mesh cells than 
> processors. The only case that's problematic is when the number of processors 
> is roughly equal or slightly less than the number of coarse mesh cells, which 
> I think is the case you run into.
> 
> If you have ideas how to improve this all, I'd be interested in working on 
> this with you!

I wouldn't even describe my case as problematic.  The partitioning works fine, 
it just struck me as unusual.  My only thought would be to pre-partition the 
coarse mesh using, e.g., METIS, and then perform a Cuthill-McKee ordering 
within the partitions.  Are there any continuity requirements for the space 
filling curve, or can we rearrange coarse cells arbitrarily?  Like I said 
though, the current strategy doesn't seem to be a problem, so this may not be 
worth the additional effort.

> 
> Best
> W.
> 
> -------------------------------------------------------------------------
> Wolfgang Bangerth                email:            [email protected]
>                                 www: http://www.math.tamu.edu/~bangerth/

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