[petsc-users] ILU preconditioner hangs with some zero elements on the diagonal

[Matthew Knepley]

On Tue, Oct 27, 2015 at 9:06 AM, Gary Rebt <gary.rebt at gmx.ch> wrote:

> Dear petsc-users,
>
> While using the FEniCS package to Solve a simple Stokes' flow problem, I
> have run into problems with PETSc preconditioners. In particular, I would
> like to use ILU (no parallel version) along with GMRES to solve my linear
> system but the solver just hangs indefinitely
> at MatLUFactorNumeric_SeqAIJ_Inode without outputting anything. CPU usage
> is at 100% but even for a tiny system (59x59 for minimal test case), the
> solver does not seem to manage to push through it after 30 mins.
>
> PETSc version is 3.6 and the matrix for the minimal test case is as
> follows :
> http://pastebin.com/t3fvdkaS
>

Hanging is a bug. We will check it out.


> It contains zero diagonal entries, has a condition number of around 1e3
> but is definitely non-singular. Direct solvers manage to solve the system
> as well as GMRES without preconditioner (although after many iterations for
> a 59x59 system..).
>

This will never work. Direct solvers work because they pivot away the
zeros, but ILU is defined by having no pivoting.

  Thanks,

     Matt


> Playing with the available options here
> http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PCILU.html
> did not seem to solve the issue (even after activating diagonal_fill and/or
> nonzeros_along_diagonal) although sometimes error 71 is returned which
> stands for zero pivot detected. Are there yet other options that I have not
> considered? The default ILU factorization in MATLAB returns satisfactory
> problems without errors so surely it must be possible with PETSc?
>
> As for the choice of ILU, I agree it might be suboptimal in this setting
> but I do need it for benchmarking purposes.
>
> Best regards,
>
> Gary
>



-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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