[petsc-users] Ordering of DoFs in submatrices with PCFieldsplit

[Matthew Knepley]

On Tue, Nov 18, 2025 at 11:12 AM Blauth, Sebastian <
sebastian.blauth at itwm.fraunhofer.de> wrote:

> Dear PETSc developers and users,
>
>
>
> I have a question regarding the Fieldsplit preconditioner in PETSc. In
> particular, I want to know how the submatrices there are created from the
> parent matrix. The “obvious” way would be to take the DoF indices of the
> corresponding split and “renumber” them so that the DoFs in the submatrix
> have the same order as the ones of the parent matrix. I did not find any
> documentation on this and as it is at least possible that the DoFs are
> re-ordered, I wanted to ask this question. Obviously, in case the DoFs are
> re-ordered, how can I get the mapping between the DoFs of the parent and
> the submatrix?
>

Hi Sebastian,

Inside, we call MatCreateSubmatrix(), which takes an IS on each process,
and selects those global rows, in the order in which they appear in the IS,
into a new parallel matrix. PCFieldsplitSetIS() can be used to specify
those IS, so you can control the reordering. Does that make sense?


> The thing I am wanting to work on is implementing a pressure convection
> diffusion preconditioner with FEniCS for the incompressible Navier-Stokes
> equations.
>
The parent matrix is assembled via a mixed FEM and then I use PETSc to
> solve the system. I want to assemble the corresponding operators on the
> pressure space from a collapsed (i.e. sub-space of the mixed FEM) function
> space. However, FEniCS re-orders the DoFs there, but I can get a mapping
> between the DoFs so this should not be problematic. However, I am not sure
> if PETSc also does a re-ordering.
>

You can just create an IS with that reordering. What operator are you
planning on assembling on the pressure space? Have you seen
https://urldefense.us/v3/__https://arxiv.org/abs/1810.03315?__;!!G_uCfscf7eWS!ZFlvrtpVlFuXdYWcwujVNh1WjnSmuEKqsh1s3GCYbyN0_wNsVgBaJo3x-lWG3Iea3iQhp_iniM9QzDSr9iD3$ 

  Thanks,

     Matt


> Thanks a lot in advance and best regards,
>
> Sebastian
>
>
>
> --
>
> Dr. Sebastian Blauth
>
> Fraunhofer-Institut für
>
> Techno- und Wirtschaftsmathematik ITWM
>
> Abteilung  Transportvorgänge
>
> Fraunhofer-Platz 1, 67663 Kaiserslautern
>
> Telefon: +49 631 31600-4968
>
> sebastian.blauth at itwm.fraunhofer.de
>
> https://urldefense.us/v3/__https://www.itwm.fraunhofer.de__;!!G_uCfscf7eWS!ZFlvrtpVlFuXdYWcwujVNh1WjnSmuEKqsh1s3GCYbyN0_wNsVgBaJo3x-lWG3Iea3iQhp_iniM9QzNhlmkaU$ 
> <https://urldefense.us/v3/__https://www.itwm.fraunhofer.de/__;!!G_uCfscf7eWS!f_qaoCRxX3prMgl6ev5fvSFQegVfZo84xW9eJTz7uYmLjZiyJFIlm1tlqYrM3LqjOpkEoMrIJZo6J63-23-atPBnJn4et_4R-UvZoWlBpHM$>
>
>
>


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https://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!ZFlvrtpVlFuXdYWcwujVNh1WjnSmuEKqsh1s3GCYbyN0_wNsVgBaJo3x-lWG3Iea3iQhp_iniM9QzGRu26U1$  <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!ZFlvrtpVlFuXdYWcwujVNh1WjnSmuEKqsh1s3GCYbyN0_wNsVgBaJo3x-lWG3Iea3iQhp_iniM9QzPGY9jGb$ >
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