[petsc-users] sees convergence with pc_fieldsplit

Thu Apr 20 14:30:43 CDT 2017

Hi, 

   I have a time-dependent multiphysics problem that I am trying to solve using pc_fieldsplit. I have defined a nested matrix for the jacobian with the diagonal block matrices explicitly created and the off-diagonal blocks defined using shell matrices, so that the matrix vector product is defined. The nonlinear system of equations at each time-step is solved using an snes construct.

    I have been facing some convergence issues, so I have reduced the problem scope to ensure that the code converges to a single discipline solution when the off-diagonal couplings are ignored.  

    Here, I have provided a constant forcing function to discipline two, which is a linear problem, so that I expect convergence in a single iteration. 

    The linear solver, defined using pc_fieldsplit seems to be converging without problems. The nonlinear solver convergence in a single time-step with FNORM in the first time step.

    The second time-step onwards, the nonlinear solver does not converge in a single step, and is terminating due to SNORM_RELATIVE. I am not sure why this is happening. 

    What is intriguing is that the solution at the end of the n^th time-step is  n times the solution after the first time step. In other words, snes at each time-step is taking the same step as was used in the first time-step. 

     Not sure sure why this is happening.  I would appreciate any advice. 

Regards,
Manav

Time step: 0 :  t = 0.000 
|| R ||_2 = 433013  : || R_i ||_2 = ( 2.81069e-07 , 433013 )
    0 KSP Residual norm 1.746840810717e-02 
    1 KSP Residual norm 5.983637077441e-12 
  Linear solve converged due to CONVERGED_RTOL iterations 1
|| R ||_2 = 5.07622e-07  : || R_i ||_2 = ( 5.07622e-07 , 7.12896e-11 )
Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1
Time step: 1 :  t = 0.001 
|| R ||_2 = 1.73186e+06  : || R_i ||_2 = ( 5.77273e-07 , 1.73186e+06 )
    0 KSP Residual norm 1.745842035995e-02 
    1 KSP Residual norm 2.366595812944e-12 
  Linear solve converged due to CONVERGED_RTOL iterations 1
|| R ||_2 = 1.29889e+06  : || R_i ||_2 = ( 9.7379e-07 , 1.29889e+06 )
Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1
Time step: 2 :  t = 0.002 :  xdot-L2 = 2.72522e-06
|| R ||_2 = 433159  : || R_i ||_2 = ( 1.35694e-06 , 433159 )
    0 KSP Residual norm 1.744848431182e-02 
    1 KSP Residual norm 7.650255893811e-12 
  Linear solve converged due to CONVERGED_RTOL iterations 1
|| R ||_2 = 866074  : || R_i ||_2 = ( 8.42454e-07 , 866074 )
Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1
Time step: 3 :  t = 0.003
|| R ||_2 = 2.59764e+06  : || R_i ||_2 = ( 1.12168e-06 , 2.59764e+06 )
    0 KSP Residual norm 1.743859969865e-02 
    1 KSP Residual norm 1.045225058356e-11 
  Linear solve converged due to CONVERGED_RTOL iterations 1
|| R ||_2 = 2.16477e+06  : || R_i ||_2 = ( 9.73157e-07 , 2.16477e+06 )
Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1

Following is the output of snesview: 
SNES Object: 1 MPI processes
  type: newtonls
  maximum iterations=50, maximum function evaluations=10000
  tolerances: relative=1e-08, absolute=1e-50, solution=1e-08
  total number of linear solver iterations=1
  total number of function evaluations=2
  norm schedule ALWAYS
  SNESLineSearch Object:   1 MPI processes
    type: basic
    maxstep=1.000000e+08, minlambda=1.000000e-12
    tolerances: relative=1.000000e-08, absolute=1.000000e-15, lambda=1.000000e-08
    maximum iterations=1
  KSP Object:   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:   1 MPI processes
    type: fieldsplit
      FieldSplit with SYMMETRIC_MULTIPLICATIVE composition: total splits = 2
      Solver info for each split is in the following KSP objects:
      Split number 0 Defined by IS
      KSP Object:      (fieldsplit_0_)       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:      (fieldsplit_0_)       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=108, cols=108
                package used to perform factorization: petsc
                total: nonzeros=2800, allocated nonzeros=2800
                total number of mallocs used during MatSetValues calls =0
                  using I-node routines: found 27 nodes, limit used is 5
        linear system matrix = precond matrix:
        Mat Object:        (fieldsplit_0_)         1 MPI processes
          type: seqaij
          rows=108, cols=108
          total: nonzeros=2800, allocated nonzeros=2800
          total number of mallocs used during MatSetValues calls =0
            using I-node routines: found 27 nodes, limit used is 5
      Split number 1 Defined by IS
      KSP Object:      (fieldsplit_1_)       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:      (fieldsplit_1_)       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 1.15385
            Factored matrix follows:
              Mat Object:               1 MPI processes
                type: seqaij
                rows=30, cols=30
                package used to perform factorization: petsc
                total: nonzeros=540, allocated nonzeros=540
                total number of mallocs used during MatSetValues calls =0
                  using I-node routines: found 9 nodes, limit used is 5
        linear system matrix = precond matrix:
        Mat Object:        (fieldsplit_1_)         1 MPI processes
          type: seqaij
          rows=30, cols=30
          total: nonzeros=468, allocated nonzeros=468
          total number of mallocs used during MatSetValues calls =0
            using I-node routines: found 10 nodes, limit used is 5
    linear system matrix = precond matrix:
    Mat Object:     1 MPI processes
      type: nest
      rows=138, cols=138
        Matrix object: 
          type=nest, rows=2, cols=2 
          MatNest structure: 
          (0,0) : prefix="fieldsplit_0_", type=seqaij, rows=108, cols=108 
          (0,1) : type=shell, rows=108, cols=30 
          (1,0) : type=shell, rows=30, cols=108 
          (1,1) : prefix="fieldsplit_1_", type=seqaij, rows=30, cols=30 

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