[petsc-users] sees convergence with pc_fieldsplit

Manav Bhatia bhatiamanav at gmail.com
Thu Apr 20 14:40:00 CDT 2017

```Hi Barry,

Attached is the output.

-Manav

|| R ||_2 = 433013  : || R_i ||_2 = ( 2.81069e-07 , 433013 )
0 SNES Function norm 4.330127018922e+05
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 )
1 SNES Function norm 5.076218984984e-07
Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1
Time step: 1 :  t = 0.001 :  xdot-L2 = 2.01301e-06
|| R ||_2 = 1.73186e+06  : || R_i ||_2 = ( 5.77273e-07 , 1.73186e+06 )
0 SNES Function norm 1.731856101521e+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 )
1 SNES Function norm 1.298892076140e+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 SNES Function norm 4.331589481273e+05
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 )
1 SNES Function norm 8.660737893156e+05
Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1
Time step: 3 :  t = 0.003 :  xdot-L2 = 3.59383e-06
|| R ||_2 = 2.59764e+06  : || R_i ||_2 = ( 1.12168e-06 , 2.59764e+06 )
0 SNES Function norm 2.597639281693e+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 )
1 SNES Function norm 2.164772029312e+06
Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1
Changing dt:  old dt = 0.001    new dt = 0.001
Time step: 4 :  t = 0.004 :  xdot-L2 = 4.9281e-06
|| R ||_2 = 1.29933e+06  : || R_i ||_2 = ( 1.2554e-06 , 1.29933e+06 )
0 SNES Function norm 1.299329216581e+06
0 KSP Residual norm 1.742876625743e-02
1 KSP Residual norm 6.512084951772e-12
Linear solve converged due to CONVERGED_RTOL iterations 1
|| R ||_2 = 1.73215e+06  : || R_i ||_2 = ( 1.00171e-06 , 1.73215e+06 )
1 SNES Function norm 1.732147071753e+06
Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1

> On Apr 20, 2017, at 2:38 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
>
>
>   Run with -snes_monitor also and send the output
>
>
>> On Apr 20, 2017, at 2:30 PM, Manav Bhatia <bhatiamanav at gmail.com> wrote:
>>
>> 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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