[petsc-users] Configure nested PCFIELDSPLIT with general index sets

[Natacha BEREUX]

Dear PETSc user's,
I am trying to solve a poroelasticity problem with an additional
temperature equation. The problem is a 3 fields problem involving  a
displacement field (u), a pressure field (p) and a temperature field (t).
I have seen similar examples in
http://www.mcs.anl.gov/papers/P2017-0112.pdf
or in Matt's talk
http://www.caam.rice.edu/~mk51/presentations/SIAMCSE13.pdf
I would like to reproduce them, but I am encountering  troubles whem trying
to do so.
Here is how I proceed:

I have a monolithic matrix A stemming .
I build 3 index sets for u,p, and t in A.
Then I set up the KSP context :

call KSPCreate(PETSC_COMM_WORLD,ksp,ierr)
call KSPSetOperators(ksp,A,A,ierr)
call KSPGetPC(ksp, pc, ierr)
call PCSetType(pc, PCFIELDSPLIT, ierr)
call PCFieldSplitSetIS(pc,'u',is_u, ierr)
call PCFieldSplitSetIS(pc,'p',is_p, ierr)
call PCFieldSplitSetIS(pc,'t',is_t, ierr)
call PCSetFromOptions(pc,ierr)
call KSPSetFromOptions(ksp,ierr)
call KSPSolve(ksp,b,x,ierr)

I run the code with the following options
-ksp_view
-log_view
-ksp_rtol 1.0e-5
-ksp_type fgmres
-pc_type fieldsplit
-pc_fieldsplit_type additive
-pc_fieldsplit_0_fields 0,1
-pc_fieldsplit_1_fields 2
-pc_fieldsplit_0_pc_type lu
-pc_fieldsplit_0_ksp_type preonly
-pc_fieldsplit_1_pc_type lu
-pc_fieldsplit_1_ksp_type preonly

I would like to group u and p fields  in a "0" block and then temperature
remains in "1" block.
(I start with direct solves in each blocks to check the block decomposition
but I intend to do use iterative methods later, and more precisely to use a
Schur fieldsplit preconditionner for the "0" block)
The output follows :

KSP Object: 1 MPI processes
  type: fgmres
    GMRES: restart=30, using Classical (unmodified) Gram-Schmidt
Orthogonalization with no iterative refinement
    GMRES: happy breakdown tolerance 1e-30
  maximum iterations=10000, initial guess is zero
  tolerances:  relative=1e-05, absolute=1e-50, divergence=10000.
  right preconditioning
  using UNPRECONDITIONED norm type for convergence test
PC Object: 1 MPI processes
  type: fieldsplit
    FieldSplit with ADDITIVE composition: total splits = 3
    Solver info for each split is in the following KSP objects:
    Split number 0 Defined by IS
    KSP Object:    (fieldsplit_u_)     1 MPI processes
      type: preonly
      maximum iterations=10000, initial guess is zero
      tolerances:  relative=1e-05, absolute=1e-50, divergence=10000.
      left preconditioning
      using DEFAULT norm type for convergence test
    PC Object:    (fieldsplit_u_)     1 MPI processes
      type: ilu
      PC has not been set up so information may be incomplete
        ILU: out-of-place factorization
        0 levels of fill
        tolerance for zero pivot 2.22045e-14
        matrix ordering: natural
      linear system matrix = precond matrix:
      Mat Object:      (fieldsplit_u_)       1 MPI processes
        type: seqaij
        rows=60, cols=60
        total: nonzeros=3600, allocated nonzeros=3600
        total number of mallocs used during MatSetValues calls =0
          using I-node routines: found 12 nodes, limit used is 5
    Split number 1 Defined by IS
    KSP Object:    (fieldsplit_p_)     1 MPI processes
      type: preonly
      maximum iterations=10000, initial guess is zero
      tolerances:  relative=1e-05, absolute=1e-50, divergence=10000.
      left preconditioning
      using DEFAULT norm type for convergence test
    PC Object:    (fieldsplit_p_)     1 MPI processes
      type: ilu
      PC has not been set up so information may be incomplete
        ILU: out-of-place factorization
        0 levels of fill
        tolerance for zero pivot 2.22045e-14
        matrix ordering: natural
      linear system matrix = precond matrix:
      Mat Object:      (fieldsplit_p_)       1 MPI processes
        type: seqaij
        rows=8, cols=8
        total: nonzeros=64, allocated nonzeros=64
        total number of mallocs used during MatSetValues calls =0
          using I-node routines: found 2 nodes, limit used is 5
    Split number 2 Defined by IS
    KSP Object:    (fieldsplit_t_)     1 MPI processes
      type: preonly
      maximum iterations=10000, initial guess is zero
      tolerances:  relative=1e-05, absolute=1e-50, divergence=10000.
      left preconditioning
      using DEFAULT norm type for convergence test
    PC Object:    (fieldsplit_t_)     1 MPI processes
      type: ilu
      PC has not been set up so information may be incomplete
        ILU: out-of-place factorization
        0 levels of fill
        tolerance for zero pivot 2.22045e-14
        matrix ordering: natural
      linear system matrix = precond matrix:
      Mat Object:      (fieldsplit_t_)       1 MPI processes
        type: seqaij
        rows=8, cols=8
        total: nonzeros=64, allocated nonzeros=64
        total number of mallocs used during MatSetValues calls =0
          using I-node routines: found 2 nodes, limit used is 5
  linear system matrix = precond matrix:
  Mat Object:   1 MPI processes
    type: seqaij
    rows=76, cols=76
    total: nonzeros=5776, allocated nonzeros=5776
    total number of mallocs used during MatSetValues calls =0
      using I-node routines: found 16 nodes, limit used is 5

The preconditionner has 3 splits, whereas I would like to group (u,p)
together and see 2 splits
I suspect that
-pc_fieldsplit_0_fields 0,1
-pc_fieldsplit_1_fields 2
are not the appropriate options.
Am I correct ?
What is the right way for grouping two fields defined by index sets ?

Any help would be greatly appreciated !

Natacha
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