[petsc-users] Block unstructured grid

[Matthew Knepley]

On Thu, Mar 11, 2021 at 3:27 AM Mathieu Dutour <mathieu.dutour at gmail.com>
wrote:

> Dear all,
>
> I would like to work with a special kind of linear system that ought to be
> very common but I am not sure that it is possible in PETSC.
>
> What we have is an unstructured grid with say 3.10^5 nodes in it.
> At each node, we have a number of frequency/direction and together
> this makes about 1000 values at the node. So, in total the linear system
> has say 3.10^8 values.
>
> We managed to implement this system with Petsc but the performance
> was unsatisfactory. We think that Petsc is not exploiting the special
> structure of the matrix and we wonder if this structure can be implemented
> in Petsc.
>
> By special structure we mean the following. An entry in the linear system
> is of the form (i, j) with 1<=i<=1000 and 1<=j<=N   with N = 3.10^5.
> The node (i , j) is adjacent to all the nodes (i' , j) and thus they make
> a block
> diagonal entry. But the node (i , j) is also adjacent to some nodes (i ,
> j')
> [About 6 such nodes, but it varies].
>

I do not understand this explanation "(i, j) with 1<=i<=1000 and 1<=j<=N".
Your linear system is rectangular of size (1000, N)? Do you mean instead
that each
entry in the linear system (i, j) is a 1000x1000 block?

We might have something that can help. If the structure of each entry is
the same, we
have this class


https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MATKAIJ.html

This would be writing the system as a Kronecker product

  A \otimes T

where T is your 1000x1000 matrix. We have only run this for moderate size
T, say 16x16,
so further optimizations might be necessary, but it is a place to start.

Is it possible to write your system in this way?

  Thanks,

     Matt


> Would there be a way to exploit this special structure in Petsc? I think
> this should be fairly common and significant speedup could be obtained.
>
> Best,
>
>   Mathieu
>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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