[petsc-users] Using the PCASM interface to define minimally overlapping subdomains

[Barry Smith]

   Patrick,

     This "local part of the subdomains for this processor” term in  PCASMSetLocalSubdomains is, IMHO, extremely confusing. WTHWTS? Anyways, I think that if you set the is_local[] to be different than the is[] you will always end up with a nonsymetric preconditioner. I think for one dimension you need to use 

> is[0] <-- 0 1 2 3
> is[1] <-- 3 4 5 6
> is_local[0] <-- 0 1 2 3
> is_local[1] <-- 3 4 5 6

Or you can pass NULL for is_local use PCASMSetOverlap(pc,0);

  Barry


Note that is_local[] doesn’t have to be non-overlapping or anything.


On Sep 16, 2014, at 10:48 AM, Patrick Sanan <patrick.sanan at gmail.com> wrote:

> For the purposes of reproducing an example from a paper, I'd like to use PCASM with subdomains which 'overlap minimally' (though this is probably never a good idea in practice).
> 
> In one dimension with 7 unknowns and 2 domains, this might look like
> 
> 0  1  2  3  4  5  6  (unknowns)
> ------------          (first subdomain  : 0 .. 3)
>         -----------  (second subdomain : 3 .. 6)
> 
> The subdomains share only a single grid point, which differs from the way PCASM is used in most of the examples.
> 
> In two dimensions, minimally overlapping rectangular subdomains would overlap one exactly one row or column of the grid. Thus, for example, if the grid unknowns were
> 
> 0  1  2  3  4  5  |
> 6  7  8  9  10 11 | |
> 12 13 14 15 16 17   |
>         --------
> -----------
> 
> then one minimally-overlapping set of 4 subdomains would be
> 0 1 2 3 6 7 8 9
> 3 4 5 9 10 11
> 6 7 8 9 12 13 14 15
> 9 10 11 15 16 17
> as suggested by the dashes and pipes above. The subdomains only overlap by a single row or column of the grid.
> 
> My question is whether and how one can use the PCASM interface to work with these sorts of decompositions (It's fine for my purposes to use a single MPI process). In particular, I don't quite understand if should be possible to define these decompositions by correctly providing is and is_local arguments to PCASMSetLocalSubdomains.
> 
> I have gotten code to run defining the is_local entries to be subsets of the is entries which define a partition of the global degrees of freedom*, but I'm not certain that this was the correct choice, as it appears to produce an unsymmetric preconditioner for a symmetric system when I use direct subdomain solves and the 'basic' type for PCASM.
> 
> * For example, in the 1D example above this would correspond to
> is[0] <-- 0 1 2 3
> is[1] <-- 3 4 5 6
> is_local[0] <-- 0 1 2
> is_local[1] <-- 3 4 5 6
> 
> 
> 
>