[petsc-users] KSP solver always has Zero pivot in LU

[Sharp Stone]

Hi Barry,

Thank you very much for your reply. They are illustrating.

I use LU and gmres in the solver. When I use a rather small size of grids,
the KSP solver works fine. However, when a larger domain is used (still
small in the problem I'm trying to solve), I still got the error "Zero
pivot in LU factorization" from Petsc.  As you previously suggested, I
solved the problem in Matlab, and got the solution, though the matrix is
close to singular. Do I have any options to solve such a system with Petsc?
For the completeness, I attached the matrix and rhs vector, and look
forward to hearing from you. Thank you in advance!

On Mon, Oct 20, 2014 at 11:38 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:

>
>   What exact options are you running with?  I tried ILU and LU and all was
> fine.
>
> $ ./ex10 -f0 ~/Desktop/binaryoutput -rhs 0 -mat_view -pc_type lu -ksp_view
> Mat Object: 1 MPI processes
>   type: seqaij
> row 0: (0, 1)  (1, 0)  (3, 0)
> row 1: (0, 0)  (1, 1)  (2, 0)  (4, 0)
> row 2: (1, 0)  (2, 1)  (5, 0)
> row 3: (0, -0.219298)  (3, 1)  (4, -0.561404)  (6, -0.219298)
> row 4: (1, -0.304878)  (3, -0.097561)  (4, 1)  (5, -0.292683)  (7,
> -0.304878)
> row 5: (2, 0)  (4, 0)  (5, 1)  (8, 0)
> row 6: (3, 0)  (6, 1)  (7, 0)
> row 7: (4, 0)  (6, 0)  (7, 1)  (8, 0)
> row 8: (5, 0)  (7, 0)  (8, 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: lu
>     LU: out-of-place factorization
>     tolerance for zero pivot 2.22045e-14
>     matrix ordering: nd
>     factor fill ratio given 5, needed 1.54545
>       Factored matrix follows:
>         Mat Object:         1 MPI processes
>           type: seqaij
>           rows=9, cols=9
>           package used to perform factorization: petsc
>           total: nonzeros=51, allocated nonzeros=51
>           total number of mallocs used during MatSetValues calls =0
>             not using I-node routines
>   linear system matrix = precond matrix:
>   Mat Object:   1 MPI processes
>     type: seqaij
>     rows=9, cols=9
>     total: nonzeros=33, allocated nonzeros=33
>     total number of mallocs used during MatSetValues calls =0
>       not using I-node routines
> Number of iterations =   1
>   Residual norm < 1.e-12
> ~/Src/petsc/src/ksp/ksp/examples/tutorials (barry/fix-setters *)
> $ ./ex10 -f0 ~/Desktop/binaryoutput -rhs 0 -mat_view -pc_type ilu -ksp_view
> Mat Object: 1 MPI processes
>   type: seqaij
> row 0: (0, 1)  (1, 0)  (3, 0)
> row 1: (0, 0)  (1, 1)  (2, 0)  (4, 0)
> row 2: (1, 0)  (2, 1)  (5, 0)
> row 3: (0, -0.219298)  (3, 1)  (4, -0.561404)  (6, -0.219298)
> row 4: (1, -0.304878)  (3, -0.097561)  (4, 1)  (5, -0.292683)  (7,
> -0.304878)
> row 5: (2, 0)  (4, 0)  (5, 1)  (8, 0)
> row 6: (3, 0)  (6, 1)  (7, 0)
> row 7: (4, 0)  (6, 0)  (7, 1)  (8, 0)
> row 8: (5, 0)  (7, 0)  (8, 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: ilu
>     ILU: out-of-place factorization
>     0 levels of fill
>     tolerance for zero pivot 2.22045e-14
>     using diagonal shift on blocks to prevent zero pivot [INBLOCKS]
>     matrix ordering: natural
>     factor fill ratio given 1, needed 1
>       Factored matrix follows:
>         Mat Object:         1 MPI processes
>           type: seqaij
>           rows=9, cols=9
>           package used to perform factorization: petsc
>           total: nonzeros=33, allocated nonzeros=33
>           total number of mallocs used during MatSetValues calls =0
>             not using I-node routines
>   linear system matrix = precond matrix:
>   Mat Object:   1 MPI processes
>     type: seqaij
>     rows=9, cols=9
>     total: nonzeros=33, allocated nonzeros=33
>     total number of mallocs used during MatSetValues calls =0
>       not using I-node routines
> Number of iterations =   2
>   Residual norm < 1.e-12
>
>
> > On Oct 20, 2014, at 10:02 PM, Sharp Stone <thronesf at gmail.com> wrote:
> >
> > Dear All,
> >
> > Last week I raised a question about KSP solver with zero pivot problem.
> Now I downsized the matrix in my problem and still got the zero pivot
> problem. I looked at the matrix and computed its eigenvalues in matlab, and
> it seems the matrix is good (not singular, I mean), but petsc still
> reported zero pivot in LU factorization. What could possibly cause this?
> Thank you very much in advance!
> >
> > PS: I attached the matrix output in my simplest test.
> >
> > --
> > Best regards,
> >
> > Feng
> > <binaryoutput>
>
>


-- 
Best regards,

Feng
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