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.
Hope this helps.
Best,
Leonardo
Il giorno gio 4 mag 2023 alle ore 18:05 Matthew Knepley <knep...@gmail.com>
ha scritto:
> On Thu, May 4, 2023 at 11:24 AM LEONARDO MUTTI <
> leonardo.mutt...@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 <bsm...@petsc.dev>
>> ha scritto:
>>
>>>
>>> Thank you for the test code. I have a fix in the branch
>>> barry/2023-04-29/fix-pcasmcreatesubdomains2d
>>> <https://gitlab.com/petsc/petsc/-/commits/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
>>> git checkout barry/2023-04-29/fix-pcasmcreatesubdomains2d
>>> <https://gitlab.com/petsc/petsc/-/commits/barry/2023-04-29/fix-pcasmcreatesubdomains2d>
>>> ./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.mutt...@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
>
> https://www.cse.buffalo.edu/~knepley/
> <http://www.cse.buffalo.edu/~knepley/>
>
