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

[Karthikeyan Chockalingam - STFC UKRI via petsc-users]

 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 <knep...@gmail.com>
Date: Tuesday, 18 April 2023 at 16:21
To: Chockalingam, Karthikeyan (STFC,DL,HC) <karthikeyan.chockalin...@stfc.ac.uk>
Cc: petsc-users@mcs.anl.gov <petsc-users@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.chockalin...@stfc.ac.uk<mailto:karthikeyan.chockalin...@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 <knep...@gmail.com<mailto:knep...@gmail.com>>
Date: Tuesday, 18 April 2023 at 11:08
To: Chockalingam, Karthikeyan (STFC,DL,HC) 
<karthikeyan.chockalin...@stfc.ac.uk<mailto:karthikeyan.chockalin...@stfc.ac.uk>>
Cc: petsc-users@mcs.anl.gov<mailto:petsc-users@mcs.anl.gov> 
<petsc-users@mcs.anl.gov<mailto:petsc-users@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@mcs.anl.gov<mailto:petsc-users@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/>