[petsc-users] strange convergence

[Barry Smith]

   Huge preconditioned norms but normal unpreconditioned norms almost always come from a very small pivot in an LU or ILU factorization. 

   The first thing to do is monitor the two sub solves. Run with the additional options -fieldsplit_u_ksp_type richardson -fieldsplit_u_ksp_monitor -fieldsplit_u_ksp_max_it 1 -fieldsplit_wp_ksp_type richardson -fieldsplit_wp_ksp_monitor -fieldsplit_wp_ksp_max_it 1

> On Apr 23, 2017, at 12:22 PM, Hoang Giang Bui <hgbk2008 at gmail.com> wrote:
> 
> Hello
> 
> I encountered a strange convergence behavior that I have trouble to understand
> 
> KSPSetFromOptions completed
>   0 KSP preconditioned resid norm 1.106709687386e+31 true resid norm 9.015150491938e+06 ||r(i)||/||b|| 1.000000000000e+00
>   1 KSP preconditioned resid norm 2.933141742664e+29 true resid norm 9.015152282123e+06 ||r(i)||/||b|| 1.000000198575e+00
>   2 KSP preconditioned resid norm 9.686409637174e+16 true resid norm 9.015354521944e+06 ||r(i)||/||b|| 1.000022631902e+00
>   3 KSP preconditioned resid norm 4.219243615809e+15 true resid norm 9.017157702420e+06 ||r(i)||/||b|| 1.000222648583e+00
> .....
> 999 KSP preconditioned resid norm 3.043754298076e+12 true resid norm 9.015425041089e+06 ||r(i)||/||b|| 1.000030454195e+00
> 1000 KSP preconditioned resid norm 3.043000287819e+12 true resid norm 9.015424313455e+06 ||r(i)||/||b|| 1.000030373483e+00
> Linear solve did not converge due to DIVERGED_ITS iterations 1000
> KSP Object: 4 MPI processes
>   type: gmres
>     GMRES: restart=1000, using Modified Gram-Schmidt Orthogonalization
>     GMRES: happy breakdown tolerance 1e-30
>   maximum iterations=1000, initial guess is zero
>   tolerances:  relative=1e-20, absolute=1e-09, divergence=10000
>   left preconditioning
>   using PRECONDITIONED norm type for convergence test
> PC Object: 4 MPI processes
>   type: fieldsplit
>     FieldSplit with 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_u_)     4 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_u_)     4 MPI processes
>       type: hypre
>         HYPRE BoomerAMG preconditioning
>         HYPRE BoomerAMG: Cycle type V
>         HYPRE BoomerAMG: Maximum number of levels 25
>         HYPRE BoomerAMG: Maximum number of iterations PER hypre call 1
>         HYPRE BoomerAMG: Convergence tolerance PER hypre call 0
>         HYPRE BoomerAMG: Threshold for strong coupling 0.6
>         HYPRE BoomerAMG: Interpolation truncation factor 0
>         HYPRE BoomerAMG: Interpolation: max elements per row 0
>         HYPRE BoomerAMG: Number of levels of aggressive coarsening 0
>         HYPRE BoomerAMG: Number of paths for aggressive coarsening 1
>         HYPRE BoomerAMG: Maximum row sums 0.9
>         HYPRE BoomerAMG: Sweeps down         1
>         HYPRE BoomerAMG: Sweeps up           1
>         HYPRE BoomerAMG: Sweeps on coarse    1
>         HYPRE BoomerAMG: Relax down          symmetric-SOR/Jacobi
>         HYPRE BoomerAMG: Relax up            symmetric-SOR/Jacobi
>         HYPRE BoomerAMG: Relax on coarse     Gaussian-elimination
>         HYPRE BoomerAMG: Relax weight  (all)      1
>         HYPRE BoomerAMG: Outer relax weight (all) 1
>         HYPRE BoomerAMG: Using CF-relaxation
>         HYPRE BoomerAMG: Measure type        local
>         HYPRE BoomerAMG: Coarsen type        PMIS
>         HYPRE BoomerAMG: Interpolation type  classical
>       linear system matrix = precond matrix:
>       Mat Object:      (fieldsplit_u_)       4 MPI processes
>         type: mpiaij
>         rows=938910, cols=938910, bs=3
>         total: nonzeros=8.60906e+07, allocated nonzeros=8.60906e+07
>         total number of mallocs used during MatSetValues calls =0
>           using I-node (on process 0) routines: found 78749 nodes, limit used is 5
>     Split number 1 Defined by IS
>     KSP Object:    (fieldsplit_wp_)     4 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_wp_)     4 MPI processes
>       type: lu
>         LU: out-of-place factorization
>         tolerance for zero pivot 2.22045e-14
>         matrix ordering: natural
>         factor fill ratio given 0, needed 0
>           Factored matrix follows:
>             Mat Object:             4 MPI processes
>               type: mpiaij
>               rows=34141, cols=34141
>               package used to perform factorization: pastix
>             Error :                        -nan
>   Error :                        -nan
>     total: nonzeros=0, allocated nonzeros=0
>             Error :                        -nan
>     total number of mallocs used during MatSetValues calls =0
>                 PaStiX run parameters:
>                   Matrix type :                      Symmetric
>                   Level of printing (0,1,2):         0
>                   Number of refinements iterations : 0
>   Error :                        -nan
>       linear system matrix = precond matrix:
>       Mat Object:      (fieldsplit_wp_)       4 MPI processes
>         type: mpiaij
>         rows=34141, cols=34141
>         total: nonzeros=485655, allocated nonzeros=485655
>         total number of mallocs used during MatSetValues calls =0
>           not using I-node (on process 0) routines
>   linear system matrix = precond matrix:
>   Mat Object:   4 MPI processes
>     type: mpiaij
>     rows=973051, cols=973051
>     total: nonzeros=9.90037e+07, allocated nonzeros=9.90037e+07
>     total number of mallocs used during MatSetValues calls =0
>       using I-node (on process 0) routines: found 78749 nodes, limit used is 5
> 
> The pattern of convergence gives a hint that this system is somehow bad/singular. But I don't know why the preconditioned error goes up too high. Anyone has an idea?
> 
> Best regards
> Giang Bui
>