Interesting, a priori I'm not sure this will work better, mainly because I'd lose the compact band structure.

As for waveform relaxation: I excluded it at first since it appears to be requiring too many CPUs than I have to beat sequential solvers, plus it is more complicated and I have very limited time at this project.

For both suggestions, because of the way the space-time matrix is generated, it is much more convenient for me to mess with the time dimension than with space. 

Overall GASM seems a simpler way to go before trying other things.
Please let me know if you decide to add the GASM interfaces.

Thanks again. 
Best,
Leonardo

Il ven 5 mag 2023, 00:01 Matthew Knepley <knepley@gmail.com> ha scritto:
On Thu, May 4, 2023 at 1:43 PM LEONARDO MUTTI <leonardo.mutti01@universitadipavia.it> wrote:
Of course, I'll try to explain.

I am solving a parabolic equation with space-time FEM and I want an efficient solver/preconditioner for the resulting system.
The corresponding matrix, call it X, has an e.g. block bi-diagonal structure, if the cG(1)-dG(0) method is used (i.e. implicit Euler solved in batch).
Every block-row of X corresponds to a time instant.

I want to introduce parallelism in time by subdividing X into overlapping submatrices of e.g 2x2 or 3x3 blocks, along the block diagonal.
For instance, call X_i the individual blocks. The submatrices would be, for various i, (X_{i-1,i-1},X_{i-1,i};X_{i,i-1},X_{i,i}).
I'd like each submatrix to be solved in parallel, to combine the various results together in an ASM like fashion.
Every submatrix has thus a predecessor and a successor, and it overlaps with both, so that as far as I could understand, GASM has to be used in place of ASM.

Yes, ordered that way you need GASM. I wonder if inverting the ordering would be useful, namely putting the time index on the inside.
Then the blocks would be over all time, but limited space, which is more the spirit of ASM I think.

Have you considered waveform relaxation for this problem?

   Thanks,

     Matt
 
Hope this helps.
Best,
Leonardo

Il giorno gio 4 mag 2023 alle ore 18:05 Matthew Knepley <knepley@gmail.com> ha scritto:
On Thu, May 4, 2023 at 11:24 AM LEONARDO MUTTI <leonardo.mutti01@universitadipavia.it> wrote:
Thank you for the help. 
Adding to my example:
      call PCGASMSetSubdomains(pc,NSub, subdomains_IS, inflated_IS,ierr)
      call PCGASMDestroySubdomains(NSub,subdomains_IS,inflated_IS,ierr)
results in:
      Error LNK2019 unresolved external symbol PCGASMDESTROYSUBDOMAINS referenced in function ...  
      Error LNK2019 unresolved external symbol PCGASMSETSUBDOMAINS referenced in function ...  
I'm not sure if the interfaces are missing or if I have a compilation problem.

I just want to make sure you really want GASM. It sounded like you might able to do what you want just with ASM.
Can you tell me again what you want to do overall?

  Thanks,

    Matt
 
Thank you again. 
Best,
Leonardo

Il giorno sab 29 apr 2023 alle ore 20:30 Barry Smith <bsmith@petsc.dev> ha scritto:

   Thank you for the test code. I have a fix in the branch  barry/2023-04-29/fix-pcasmcreatesubdomains2d with merge request https://gitlab.com/petsc/petsc/-/merge_requests/6394

   The functions did not have proper Fortran stubs and interfaces so I had to provide them manually in the new branch.

   Use

   git fetch
   ./configure etc

   Your now working test code is in src/ksp/ksp/tests/ex71f.F90  I had to change things slightly and I updated the error handling for the latest version.

   Please let us know if you have any later questions.

  Barry




On Apr 28, 2023, at 12:07 PM, LEONARDO MUTTI <leonardo.mutti01@universitadipavia.it> wrote:

Hello. I am having a hard time understanding the index sets to feed PCGASMSetSubdomains, and I am working in Fortran (as a PETSc novice). To get more intuition on how the IS objects behave I tried the following minimal (non) working example, which should tile a 16x16 matrix into 16 square, non-overlapping submatrices:

#include <petsc/finclude/petscmat.h>
#include <petsc/finclude/petscksp.h>
#include <petsc/finclude/petscpc.h>
      USE petscmat
      USE petscksp
      USE petscpc
      
      Mat   :: A
      PetscInt :: M, NSubx, dof, overlap, NSub
      INTEGER :: I,J
      PetscErrorCode      :: ierr
      PetscScalar :: v
      KSP            :: ksp
      PC             :: pc
      IS :: subdomains_IS, inflated_IS
     
      call PetscInitialize(PETSC_NULL_CHARACTER , ierr)
      
!-----Create a dummy matrix
      M = 16
      call MatCreateAIJ(MPI_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE,
     & M, M,
     & PETSC_DEFAULT_INTEGER, PETSC_NULL_INTEGER,
     & PETSC_DEFAULT_INTEGER, PETSC_NULL_INTEGER,
     & A, ierr)
     
      DO I=1,M
         DO J=1,M
            v = I*J
            CALL MatSetValue (A,I-1,J-1,v,
     &                     INSERT_VALUES , ierr)
         END DO
      END DO
     
      call MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY , ierr)
      call MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY , ierr)
      
!-----Create KSP and PC
      call KSPCreate(PETSC_COMM_WORLD,ksp, ierr)
      call KSPSetOperators(ksp,A,A, ierr)
      call KSPSetType(ksp,"bcgs",ierr)
      call KSPGetPC(ksp,pc,ierr)
      call KSPSetUp(ksp, ierr)
      call PCSetType(pc,PCGASM, ierr)
      call PCSetUp(pc , ierr)
     
!-----GASM setup
      NSubx = 4
      dof = 1
      overlap = 0
     
      call PCGASMCreateSubdomains2D(pc,
     &      M, M,
     &      NSubx, NSubx,
     &      dof, overlap,
     &      NSub, subdomains_IS, inflated_IS, ierr)

      call ISView(subdomains_IS, PETSC_VIEWER_STDOUT_WORLD, ierr)
     
      call KSPDestroy(ksp, ierr)  
      call PetscFinalize(ierr)

Running this on one processor, I get NSub = 4.
If PCASM and PCASMCreateSubdomains2D are used instead, I get NSub = 16 as expected.
Moreover, I get in the end "forrtl: severe (157): Program Exception - access violation". So:
1) why do I get two different results with ASM, and GASM?
2) why do I get access violation and how can I solve this?
In fact, in C, subdomains_IS, inflated_IS should pointers to IS objects. As I see on the Fortran interface, the arguments to PCGASMCreateSubdomains2D are IS objects:

       subroutine PCGASMCreateSubdomains2D(a,b,c,d,e,f,g,h,i,j,z)
       import tPC,tIS
       PC a ! PC
       PetscInt b ! PetscInt
       PetscInt c ! PetscInt
       PetscInt d ! PetscInt
       PetscInt e ! PetscInt
       PetscInt f ! PetscInt
       PetscInt g ! PetscInt
       PetscInt h ! PetscInt
       IS i ! IS
       IS j ! IS
       PetscErrorCode z
       end subroutine PCGASMCreateSubdomains2D
Thus:
3) what should be inside e.g., subdomains_IS? I expect it to contain, for every created subdomain, the list of rows and columns defining the subblock in the matrix, am I right?

Context: I have a block-tridiagonal system arising from space-time finite elements, and I want to solve it with GMRES+PCGASM preconditioner, where each overlapping submatrix is on the diagonal and of size 3x3 blocks (and spanning multiple processes). This is PETSc 3.17.1 on Windows.

Thanks in advance,
Leonardo



--
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



--
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