[petsc-dev] Block system

[Matthew Knepley]

On Mon, Feb 13, 2017 at 9:46 AM, Pierre Jolivet <Pierre.Jolivet at enseeiht.fr>
wrote:

> Hello,
> Given this block matrix:
> A = [A11,A12,A13,A14;
>      A21,A22,A23,A24;
>      A31,A32,A33,A34;
>      A41,A42,A43,A44];
> It is trivial to precondition Ax = b with M^-1 = diag(A11^-1, A22^-1,
> A33^-1, A44^-1);
> My application requires a slightly fancier preconditionner which should be
> M^-1 = diag(inv([A11,A12;A21,A22]),inv([A33,A34;A43,A44]));
> I'm not sure what is the right tool for this.
> I've stopped at a 4x4 block matrix, but at scale I have a matrix with few
> thousands x few thousands blocks (still with the nested 2 x 2 block
> structure).
>
> 1) should I implement a PCSHELL myself, or use a fieldsplit preconditioner
> with "few thousands / 2" fields (i.e., does PCFIELDSPLIT scale relatively
> well with the number of fields, or do you recommend it only for
> "Stokes-like" problems?)?
>

FieldSplit is not that scalable right now (I think). For 4x4 blocks, you
want to solve 8x8 systems. You could use MATBAIJ with block size 8 and
then PBJACOBI. Would that work for you?

  Thanks,

     Matt


> 2) I gave PCFIELDSPLIT a go, but I'm failing miserably. In the attached
> tarball, I'm loading matrix A on four processes. Each process owns 2 rows
> of A. I'm thus creating two ISes:
>

I will look at this as soon as I can, but I am really swamped right now.

  Matt


> IS Object: 4 MPI processes
>   type: general
> [0] Number of indices in set 2
> [0] 0 0
> [0] 1 1
> [1] Number of indices in set 2
> [1] 0 2
> [1] 1 3
> [2] Number of indices in set 0
> [3] Number of indices in set 0
> IS Object: 4 MPI processes
>   type: general
> [0] Number of indices in set 0
> [1] Number of indices in set 0
> [2] Number of indices in set 2
> [2] 0 4
> [2] 1 5
> [3] Number of indices in set 2
> [3] 0 6
> [3] 1 7
>
> which looks good to me. But when I run:
> $ mpirun -np 4 ./a.out -f almost_full_jolivet -pc_type fieldsplit
> -pc_fieldsplit_type additive -fieldsplit_ksp_type preonly
> -fieldsplit_pc_type lu -fieldsplit_pc_factor_mat_solver_package mumps
> It fails during setup:
> [0]PETSC ERROR: Petsc has generated inconsistent data
> [0]PETSC ERROR: Unhandled case, must have at least two fields, not 1
>
> I would appreciate any feedback and/or fix for this.
> Thanks, and feel free to move the thread to petsc-users.
> Pierre




-- 
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
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