[petsc-users] Setting up a matrix for Lagrange multiplier

[Matthew Knepley]

On Mon, Apr 24, 2023 at 10:22 AM Karthikeyan Chockalingam - STFC UKRI <
karthikeyan.chockalingam at stfc.ac.uk> wrote:

> Hello,
>
>
>
> I was able to construct the below K matrix (using submatrices P and P^T),
> which is of type MATAIJ
>
> K = [A P^T
>
>        P   0]
>
> and solved them using a direct solver.
>

I modified your example to create either AIJ or Nest matrices, but use the
same assembly code:

  https://gitlab.com/petsc/petsc/-/merge_requests/6368


> However, I was reading online that this is a saddle point problem and I
> should be employing PCFIELDSPLIT.
>
> Since I have one monolithic matrix K, I was not sure how to split the
> fields.
>

With this particular matrix, you can use

  -pc_fieldsplit_detect_saddle_point

and it will split it automatically.

  Thanks,

     Matt


> Best regards,
>
> Karthik.
>
>
>
>
>
> *From: *Chockalingam, Karthikeyan (STFC,DL,HC) <
> karthikeyan.chockalingam at stfc.ac.uk>
> *Date: *Wednesday, 19 April 2023 at 17:52
> *To: *Matthew Knepley <knepley at gmail.com>
> *Cc: *petsc-users at mcs.anl.gov <petsc-users at mcs.anl.gov>
> *Subject: *Re: [petsc-users] Setting up a matrix for Lagrange multiplier
>
>  I have declared the mapping
>
>
>
>   ISLocalToGlobalMapping mapping;
>
>     ISLocalToGlobalMappingCreate(PETSC_COMM_WORLD, 1, n, nindices,
> PETSC_COPY_VALUES, &mapping);
>
>
>
> But when I use MatSetValuesLocal(), how do I know the above mapping is
> employed because it is not one of the parameters passed to the function?
>
>
>
> Thank you.
>
>
>
> Kind regards,
>
> Karthik.
>
>
>
>
>
> *From: *Matthew Knepley <knepley at gmail.com>
> *Date: *Tuesday, 18 April 2023 at 16:21
> *To: *Chockalingam, Karthikeyan (STFC,DL,HC) <
> karthikeyan.chockalingam at stfc.ac.uk>
> *Cc: *petsc-users at mcs.anl.gov <petsc-users at mcs.anl.gov>
> *Subject: *Re: [petsc-users] Setting up a matrix for Lagrange multiplier
>
> On Tue, Apr 18, 2023 at 11:16 AM Karthikeyan Chockalingam - STFC UKRI <
> karthikeyan.chockalingam at stfc.ac.uk> wrote:
>
> Thank you for your response. I spend some time understanding how
>
> MatSetValuesLocal and ISLocalToGlobalMappingCreate work.
>
>
>
> You can look at SNES ex28 where we do this with DMCOMPOSITE.
>
>
>
> Q1) Will the matrix K be of type MATMPIAIJ or MATIS?
>
> K = [A P^T
>
>        P   0]
>
>
>
> I assume MPIAIJ since IS is only used for Neumann-Neumann decompositions.
>
>
>
> Q2) Can I use both MatSetValues() to MatSetValuesLocal() to populate K?
> Since I have already used MatSetValues() to construct A.
>
>
>
> You can, and there would be no changes in serial if K is exactly the upper
> left block, but in parallel global indices would change.
>
>
>
> Q3) What are the advantages of using MatSetValuesLocal()? Is it that I can
> construct P directly using local indies and map the entrees to the global
> index in K?
>
>
>
> You have a monolithic K, so that you can use sparse direct solvers to
> check things. THis is impossible with separate storage.
>
>
>
> Q4) I probably don’t have to construct an independent P matrix
>
>
>
> You wouldn't in this case.
>
>
>
>   Thanks,
>
>
>
>      Matt
>
>
>
> Best regards,
>
> Karthik.
>
>
>
>
>
>
>
> *From: *Matthew Knepley <knepley at gmail.com>
> *Date: *Tuesday, 18 April 2023 at 11:08
> *To: *Chockalingam, Karthikeyan (STFC,DL,HC) <
> karthikeyan.chockalingam at stfc.ac.uk>
> *Cc: *petsc-users at mcs.anl.gov <petsc-users at mcs.anl.gov>
> *Subject: *Re: [petsc-users] Setting up a matrix for Lagrange multiplier
>
> On Tue, Apr 18, 2023 at 5:24 AM Karthikeyan Chockalingam - STFC UKRI via
> petsc-users <petsc-users at mcs.anl.gov> wrote:
>
> Hello,
>
>
>
> I'm solving a problem using the Lagrange multiplier, the matrix has the
> form
>
>
>
> K = [A P^T
>
>        P   0]
>
>
>
> I am familiar with constructing K using MATMPIAIJ. However, I would like
> to know if had [A], can I augment it with [P], [P^T] and [0] of type
> MATMPIAIJ? Likewise for vectors as well.
>
>
>
> Can you please point me to the right resource, if it is a common operation
> in PETSc?
>
>
>
> You can do this at least 2 ways:
>
>
>
>   1) Assemble you submatrices directly into the larger matrix by
> constructing local-to-global maps for the emplacement. so that you do
>
>       not change your assembly code, except to change MatSetValues() to
> MatSetValuesLocal(). This is usually preferable.
>
>
>
>   2) Use MATNEST and VecNEST to put pointers to submatrices and subvectors
> directly in.
>
>
>
>   Thanks,
>
>
>
>      Matt
>
>
>
> Many thanks.
>
>
>
> Kind regards,
>
> Karthik.
>
>
>
>
>
>
>
>
>
>
>
>
> --
>
> 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://www.cse.buffalo.edu/~knepley/
> <http://www.cse.buffalo.edu/~knepley/>
>
>
>
>
> --
>
> 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://www.cse.buffalo.edu/~knepley/
> <http://www.cse.buffalo.edu/~knepley/>
>


-- 
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://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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