[petsc-users] PCMG with PCREDISTRIBUTE

[Barry Smith]

   ex42.c provides directly the interpolation/restriction needed to move between levels in the loop

 for (k = 1; k < nlevels; k++) {
    PetscCall(DMCreateInterpolation(da_list[k - 1], da_list[k], &R, NULL));
    PetscCall(PCMGSetInterpolation(pc, k, R));
    PetscCall(MatDestroy(&R));
  }

The more standard alternative to this is to call KSPSetDM() and have the PCMG setup use the DM
to construct the interpolations (I don't know why ex42.c does this construction itself instead of having the KSPSetDM() process handle it but that doesn't matter). The end result is the same in both cases.

Since PCREDISTRIBUTE  builds its own  new matrix (by using only certain rows and columns of the original matrix) the original interpolation
cannot be used for two reasons

1) (since it is for the full system) It is for the wrong problem. 

2) In addition, if you ran with ex42.c the inner KSP does not have access to the interpolation that was constructed so you could not get PCMG to to work as indicated below.

I am guessing that your code is slightly different than ex42.c because you take the interpolation matrix provided by the DM 
and give it to the inner KSP PCMG?. So you solve problem 2 but not problem 1.

So the short answer is that there is no "canned" way to use the PCMG process trivially with PCDISTRIBUTE. 

To do what you want requires two additional steps

1) after you construct the full interpolation matrix  (by using the DM) you need to remove the rows associated with the dof that have been removed by the "locked" variables (and the columns that are associated with coarse grid points that live on the removed points) so that the interpolation is the correct "size" for the smaller problem

2) since PCREDISTRIBUTE actually moves dof of freedom between MPI processes for load balancing after it has removed the locked variables you would need to do the exact same movement for the rows of the interpolation matrix that you have constructed (after you have removed the "locked" rows of the interpolation.

Lots of bookkeeping to acheive 1 and 2 but conceptually simple.

As an experiment you can try using PCGAMG on the redistributed matrix -redistribute_pc_type gamg to use algebraic multigrid just to see the time and convergence rates. Since GAMG creates its own interpolation based on the matrix and it will be built on the smaller redistributed matrix there will no issue with the wrong "sized" interpolation. Of course you have the overhead of algebraic multigrid and cannot take advantage of geometric multigrid.  The GAMG approach may be satisfactory to your needs.

If you are game for looking more closely at using redistribute with geometric multigrid and PETSc (which will require digging into PETSc source code and using internal information in the PETSc source code) you can start by looking at how we solve variational problems with SNES using reduced space active set methods. SNESVINEWTONRSLS /src/snes/impls/vi/rs/virs.c This code solves problem 1 see DMSetVI() it builds the entire interpolation and then pulls out the required non-locked part. Reduced space active set methods essentially lock the constrained dof and solve a smaller system without those dof at each iteration.

But it does not solve problem 2. Moving the rows of the "smaller" interpolation to the correct MPI process based on where PCREDISTRIBUTE moved rows. To do this would requring looking at the PCREDISTRUBUTE code and extracting the information of where each row was moving and performing the process for the interpolation matrix.
src/ksp/pc/impls/redistribute/redistribute.c

  Barry









> On Jun 30, 2023, at 8:21 AM, Carl-Johan Thore via petsc-users <petsc-users at mcs.anl.gov> wrote:
> 
> Hi,
>  
> I'm trying to run an iterative solver (FGMRES for example) with PCMG as preconditioner. The setup of PCMG
> is done roughly as in ex42 of the PETSc-tutorials (https://petsc.org/main/src/ksp/ksp/tutorials/ex42.c.html).
> Since I have many locked  degrees-of-freedom I would like to use PCREDISTRIBUTE. However, this
> results in (30039 is the number of DOFs after redistribute and 55539 the number before):
>  
> [0]PETSC ERROR: --------------------- Error Message --------------------------------------------------------------
> [0]PETSC ERROR: Nonconforming object sizes
> [0]PETSC ERROR: Matrix dimensions of A and P are incompatible for MatProductType PtAP: A 30039x30039, P 55539x7803
> [0]PETSC ERROR: See https://petsc.org/release/faq/ for trouble shooting.
> [0]PETSC ERROR: Petsc Development GIT revision: v3.19.0-238-g512d1ae6db4  GIT Date: 2023-04-24 16:37:00 +0200
> [0]PETSC ERROR: topopt on a arch-linux-c-opt Fri Jun 30 13:28:41 2023
> [0]PETSC ERROR: Configure options COPTFLAGS="-O3 -march=native" CXXOPTFLAGS="-O3 -march=native" FOPTFLAGS="-O3 -march=native" CUDAOPTFLAGS=-O3 --with-cuda --with-cusp --with-debugging=0 --download-scalapack --download-hdf5 --download-zlib --download-mumps --download-parmetis --download-metis --download-ptscotch --download-hypre --download-spai
> [0]PETSC ERROR: #1 MatProductSetFromOptions_Private() at /mnt/c/mathware/petsc/src/mat/interface/matproduct.c:420
> [0]PETSC ERROR: #2 MatProductSetFromOptions() at /mnt/c/mathware/petsc/src/mat/interface/matproduct.c:541
> [0]PETSC ERROR: #3 MatPtAP() at /mnt/c/mathware/petsc/src/mat/interface/matrix.c:9868
> [0]PETSC ERROR: #4 MatGalerkin() at /mnt/c/mathware/petsc/src/mat/interface/matrix.c:10899
> [0]PETSC ERROR: #5 PCSetUp_MG() at /mnt/c/mathware/petsc/src/ksp/pc/impls/mg/mg.c:1029
> [0]PETSC ERROR: #6 PCSetUp() at /mnt/c/mathware/petsc/src/ksp/pc/interface/precon.c:994
> [0]PETSC ERROR: #7 KSPSetUp() at /mnt/c/mathware/petsc/src/ksp/ksp/interface/itfunc.c:406
> [0]PETSC ERROR: #8 PCSetUp_Redistribute() at /mnt/c/mathware/petsc/src/ksp/pc/impls/redistribute/redistribute.c:327
> [0]PETSC ERROR: #9 PCSetUp() at /mnt/c/mathware/petsc/src/ksp/pc/interface/precon.c:994
> [0]PETSC ERROR: #10 KSPSetUp() at /mnt/c/mathware/petsc/src/ksp/ksp/interface/itfunc.c:406
> [0]PETSC ERROR: #11 KSPSolve_Private() at /mnt/c/mathware/petsc/src/ksp/ksp/interface/itfunc.c:824
> [0]PETSC ERROR: #12 KSPSolve() at /mnt/c/mathware/petsc/src/ksp/ksp/interface/itfunc.c:1070
>  
> It’s clear what happens I think, and it kind of make since not all levels are redistributed as they should (?).
> Is it possible to use PCMG with PCREDISTRIBUTE in an easy way?
>  
> Kind regards,
> Carl-Johan

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