[petsc-users] Block unstructured grid

[Mark Adams]

Mathieu,
We have "FieldSplit" support for fields, but I don't know if it has ever
been pushed to 1000's of fields so it might fall down. It might work.
FieldSplit lets you manipulate the ordering, say field major (j) or node
major (i).
What was unsatisfactory?
It sounds like you made a rectangular matrix A(1000,3e5) . Is that correct?
Mark


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].
>
> 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
>
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