[petsc-users] MatOrdering for rectangular matrix

[Matthew Knepley]

On Thu, Oct 22, 2020 at 4:24 AM Marcel Huysegoms <m.huysegoms at fz-juelich.de>
wrote:

> Hi all,
>
> I'm currently implementing a Gauss-Newton approach for minimizing a
> non-linear cost function using PETSc4py.
> The (rectangular) linear systems I am trying to solve have dimensions of
> about (5N, N), where N is in the range of several hundred millions.
>
> Due to its size and because it's an over-determined system, I use LSQR
> in conjunction with a preconditioner (which operates on A^T x A, e.g.
> BJacobi).
> Depending on the ordering of the unknowns the algorithm only converges
> for special cases. When I use a direct LR solver (as preconditioner) it
> consistently converges, but consumes too much memory. I have read in the
> manual that the LR solver internally also applies a matrix reordering
> beforehand.
>
> My question would be:
> How can I improve the ordering of the unknowns for a rectangular matrix
> (in order to converge also with iterative preconditioners)? If I use
> MatGetOrdering(), it only works for square matrices. Is there a way to
> achieve this from within PETSc4py?
> ParMETIS seems to be a promising framework for that task. Is it possible
> to apply its reordering algorithm to a rectangular PETSc-matrix?
>
> I would be thankful for every bit of advice that might help.
>

We do not have any rectangular reordering algorithms. I think your first
step is to
find something in the literature that you think will work.

  Thanks,

     Matt


> Best regards,
> Marcel
>
>
>
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-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
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https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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