[petsc-users] solving system with 2x2 block size

[Manav Bhatia]

Hi, 

   I am setting up a matrix with the following calls. The intent is to solve the system with a 2x2 block size.

   What combinations of KSP/PC will effectively translate to solving this block matrix system? 

   I saw a discussion about bjacobi in the manual with the following calls (I omitted the prefixes from my actual command):   
-pc_type bjacobi -pc_bjacobi_blocks 2 -sub_ksp_type preonly -sub_pc_type lu  -ksp_view

which provides the following output: 
KSP Object:(fluid_complex_) 1 MPI processes
  type: gmres
    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.
  left preconditioning
  using PRECONDITIONED norm type for convergence test
PC Object:(fluid_complex_) 1 MPI processes
  type: bjacobi
    block Jacobi: number of blocks = 2
    Local solve is same for all blocks, in the following KSP and PC objects:
    KSP Object:    (fluid_complex_sub_)     1 MPI processes
      type: preonly
      maximum iterations=10000, initial guess is zero
      tolerances:  relative=1e-05, absolute=1e-50, divergence=10000.
      left preconditioning
      using NONE norm type for convergence test
    PC Object:    (fluid_complex_sub_)     1 MPI processes
      type: lu
        LU: out-of-place factorization
        tolerance for zero pivot 2.22045e-14
        matrix ordering: nd
        factor fill ratio given 5., needed 5.70941
          Factored matrix follows:
            Mat Object:             1 MPI processes
              type: seqaij
              rows=36844, cols=36844
              package used to perform factorization: petsc
              total: nonzeros=14748816, allocated nonzeros=14748816
              total number of mallocs used during MatSetValues calls =0
                using I-node routines: found 9211 nodes, limit used is 5
      linear system matrix = precond matrix:
      Mat Object:      (fluid_complex_)       1 MPI processes
        type: seqaij
        rows=36844, cols=36844
        total: nonzeros=2583248, allocated nonzeros=2583248
        total number of mallocs used during MatSetValues calls =0
          using I-node routines: found 9211 nodes, limit used is 5
  linear system matrix = precond matrix:
  Mat Object:  (fluid_complex_)   1 MPI processes
    type: seqaij
    rows=73688, cols=73688, bs=2
    total: nonzeros=5224384, allocated nonzeros=5224384
    total number of mallocs used during MatSetValues calls =0
      using I-node routines: found 18422 nodes, limit used is 5


Likewise, I tried to use a more generic option: 
-mat_set_block_size 2 -ksp_type gmres -pc_type ilu  -sub_ksp_type preonly -sub_pc_type lu  -ksp_view

with the following output:
Linear fluid_complex_ solve converged due to CONVERGED_RTOL iterations 38
KSP Object:(fluid_complex_) 1 MPI processes
  type: gmres
    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.
  left preconditioning
  using PRECONDITIONED norm type for convergence test
PC Object:(fluid_complex_) 1 MPI processes
  type: ilu
    ILU: out-of-place factorization
    0 levels of fill
    tolerance for zero pivot 2.22045e-14
    matrix ordering: natural
    factor fill ratio given 1., needed 1.
      Factored matrix follows:
        Mat Object:         1 MPI processes
          type: seqaij
          rows=73688, cols=73688, bs=2
          package used to perform factorization: petsc
          total: nonzeros=5224384, allocated nonzeros=5224384
          total number of mallocs used during MatSetValues calls =0
            using I-node routines: found 18422 nodes, limit used is 5
  linear system matrix = precond matrix:
  Mat Object:  (fluid_complex_)   1 MPI processes
    type: seqaij
    rows=73688, cols=73688, bs=2
    total: nonzeros=5224384, allocated nonzeros=5224384
    total number of mallocs used during MatSetValues calls =0
      using I-node routines: found 18422 nodes, limit used is 5

  Are other PC types expected to translate to the block matrices? 

  I would appreciate any guidance. 

Thanks,
Manav

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