[petsc-users] Ordering of DoFs in submatrices with PCFieldsplit
Matthew Knepley
knepley at gmail.com
Wed Nov 19 07:18:50 CST 2025
On Wed, Nov 19, 2025 at 2:03 AM Blauth, Sebastian <
sebastian.blauth at itwm.fraunhofer.de> wrote:
> Dear Matt,
>
> thanks for the clarification. Yes, that makes sense. Basically, I use two
> approaches for defining the splits in my code, see
> https://urldefense.us/v3/__https://github.com/sblauth/cashocs/blob/46c0d91467d03a4906b7bde29727b45d4bb0d6d2/cashocs/_utils/linalg.py*L245-L287__;Iw!!G_uCfscf7eWS!Z3vaW6mH3kTXdhSyLFZ2XcUc1E6hcY4dtjtLWLAzcg4Pj_S8issujZ0Khj24yL9Bb5KfynJ0mj5vygrOWHgH$
> I think the first one, where the IS is defined, then does exactly what I
> thought it would do. In the second approach, which I need for nested
> fieldsplits, I use a DMShell with a Section defined analogously - so I
> guess the same applies here.
>
Okay.
> Well, yes I could just reorder the DoFs for the creation of the
> submatrices - but I usually don't need these sub-functionspaces and would
> not want to create them every time. I thought of using MatPermute (
> https://urldefense.us/v3/__https://petsc.org/release/petsc4py/reference/petsc4py.PETSc.Mat.html*petsc4py.PETSc.Mat.permute__;Iw!!G_uCfscf7eWS!Z3vaW6mH3kTXdhSyLFZ2XcUc1E6hcY4dtjtLWLAzcg4Pj_S8issujZ0Khj24yL9Bb5KfynJ0mj5vyiWtyehi$ )
> with the permutation I get from FEniCS - or is there any reason not to do
> so?
>
That is more memory movement. I am not understanding why you would not just
permute the input defining the nested FS.
> And thank you very much for the reference. Yes, I am aware of the paper
> you sent. However I think the function spaces involved in the method make
> it more or less infeasible for me - usually using Taylor-Hood elements is
> already very expensive. I usually use a stabilized P1-P1 discretization or
> try to get the linear Crouzeix–Raviart with elementwise constant pressure
> working (for slow flows, this works okay, but as I go to higher Reynolds
> numbers, things become more problematic).
>
Oh, yes those spaces are crazy, but not necessary. In
https://urldefense.us/v3/__https://arxiv.org/pdf/2107.00820__;!!G_uCfscf7eWS!Z3vaW6mH3kTXdhSyLFZ2XcUc1E6hcY4dtjtLWLAzcg4Pj_S8issujZ0Khj24yL9Bb5KfynJ0mj5vysoKtJkS$ , on page 9, you can see that they are able
to prove the kernel decomposition property for simple Taylor-Hood.
> And regarding your question on which operators I am planning to assemble
> on the pressure space: Basically the pressure mass matrix, pressure
> convection-diffusion matrix and a pressure Laplacian.
>
> If you have any tips for solving the incompressible Navier Stokes
> equations (steady state) at higher Reynolds numbers I certainly welcome
> them. I can also go a bit more into detail of what kind of solution
> approach I am using - if that is appropriate here.
>
I think that the Augmented Lagrangian strategy from the Stadler paper is
currently the best option I know of.
Thanks,
Matt
> Thanks a lot 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!Z3vaW6mH3kTXdhSyLFZ2XcUc1E6hcY4dtjtLWLAzcg4Pj_S8issujZ0Khj24yL9Bb5KfynJ0mj5vyu_13JIA$
>
> > -----Original Message-----
> > From: Matthew Knepley <knepley at gmail.com>
> > Sent: Tuesday, November 18, 2025 5:23 PM
> > To: Blauth, Sebastian <sebastian.blauth at itwm.fraunhofer.de>
> > Cc: PETSc users list <petsc-users at mcs.anl.gov>
> > Subject: Re: [petsc-users] Ordering of DoFs in submatrices with
> PCFieldsplit
> >
> > On Tue, Nov 18, 2025 at 11:12 AM Blauth, Sebastian
> > <sebastian.blauth at itwm.fraunhofer.de
> > <mailto: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!Z3vaW6mH3kTXdhSyLFZ2XcUc1E6hcY4dtjtLWLAzcg4Pj_S8issujZ0Khj24yL9Bb5KfynJ0mj5vyv_7q3wU$
> >
> > 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
> > <mailto:sebastian.blauth at itwm.fraunhofer.de>
> >
> > https://urldefense.us/v3/__https://www.itwm.fraunhofer.de__;!!G_uCfscf7eWS!Z3vaW6mH3kTXdhSyLFZ2XcUc1E6hcY4dtjtLWLAzcg4Pj_S8issujZ0Khj24yL9Bb5KfynJ0mj5vyu_13JIA$
> > <
> https://urldefense.us/v3/__https://www.itwm.fraunhofer.de/__;!!G_uCfscf7eW
> > S!f_qaoCRxX3prMgl6ev5fvSFQegVfZo84xW9eJTz7uYmLjZiyJFIlm1tlqYrM3LqjOpkE
> > oMrIJZo6J63-23-atPBnJn4et_4R-UvZoWlBpHM$>
> >
> >
> >
> >
> >
> > --
> >
> > What most experimenters take for granted before they begin their
> experiments is
> > infinitely more interesting than any results to which their experiments
> lead.
> > -- Norbert Wiener
> >
> > https://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!Z3vaW6mH3kTXdhSyLFZ2XcUc1E6hcY4dtjtLWLAzcg4Pj_S8issujZ0Khj24yL9Bb5KfynJ0mj5vypAp6Vm8$
> > <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!Z3vaW6mH3kTXdhSyLFZ2XcUc1E6hcY4dtjtLWLAzcg4Pj_S8issujZ0Khj24yL9Bb5KfynJ0mj5vymdmkq01$ >
>
>
--
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://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!Z3vaW6mH3kTXdhSyLFZ2XcUc1E6hcY4dtjtLWLAzcg4Pj_S8issujZ0Khj24yL9Bb5KfynJ0mj5vypAp6Vm8$ <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!Z3vaW6mH3kTXdhSyLFZ2XcUc1E6hcY4dtjtLWLAzcg4Pj_S8issujZ0Khj24yL9Bb5KfynJ0mj5vymdmkq01$ >
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