KSPSetNullSpace and CG for singular systems

[berry]

Thanks...

Shao-Ching, have you solved this problem?


On Mon, Aug 4, 2008 at 11:49 AM, Barry Smith <bsmith at mcs.anl.gov> wrote:

>
>  One reason not to use this approach is that it can result in a very
> ill-conditioned linear
> system that may be difficult for an iterative solver.
>
>   Barry
>
>
> On Aug 3, 2008, at 10:09 PM, berry wrote:
>
>  hi, shao-ching
>>
>> Why not try to change the singular matrix to be non-singular ?
>> I mean set the last column and row of the matrix to be zero except
>> diagonal element( which is set to 1).
>>
>>
>>
>> On Mon, Aug 4, 2008 at 9:23 AM, Shao-Ching Huang <schuang at ats.ucla.edu>
>> wrote:
>> Hi Barry:
>>
>> Thanks you for your suggestions. Now both sequential and parallel
>> cases work when I use CG.
>>
>> Shao-Ching
>>
>>
>> On Fri, Aug 01, 2008 at 08:56:23PM -0500, Barry Smith wrote:
>> >
>> >    It is not the null space that is the problem.
>> >
>> >    You are right to try the shift but
>> > 1) first run on one process using -pc_type icc -ksp_type cg -
>> > pc_factor_shift_positive_definite
>> > this will keep increasing the shift until it produces a positive-
>> > definite preconditioner.
>> >
>> > Run also with -ksp_view to confirm that it is using all the options you
>> > provided. (you can run with -help to
>> > see the option names)
>> >
>> > 2) If you have the sequential converging then use -pc_type bjacobi -
>> > sub_pc_type icc -pc_factor_shift_positive_definite
>> >
>> > Barry
>> >
>> > On Aug 1, 2008, at 7:52 PM, Shao-Ching Huang wrote:
>> >
>> >> Hi,
>> >>
>> >> I am trying to use CG to solve a singular systems (i.e. Poisson
>> >> equation with periodic conditions on all boundaries).
>> >>
>> >> The code works when I use GMRES, but it diverges when I switch CG.
>> >>
>> >> Since the null space is a constant vector, in the code I have:
>> >>
>> >>   KSP ksp;
>> >>   MatNullSpace nullspace;
>> >>   ...
>> >>   MatNullSpaceCreate(MPI_COMM_WORLD, PETSC_TRUE, 0, PETSC_NULL,
>> >> &nullspace);
>> >>   KSPSetNullSpace(ksp, nullspace);
>> >>   MatNullSpaceRemove(nullspace, f->p_rhs, PETSC_NULL);
>> >>
>> >>   KSPSetFromOptions(ksp);
>> >>   KSPSetUp(ksp);
>> >>   KSPSolve(ksp, f->p_rhs, f->phi);
>> >>
>> >> [f->p_rhs is the RHS vector. f->phi is the solution vector.]
>> >>
>> >> When I use "-ksp_type gmres", it converges (shown by -ksp_monitor).
>> >>
>> >> However, when I switch to "-ksp_type cg", it diverges.
>> >> In this case (cg), "-ksp_converged_reason" says:
>> >>
>> >>  Linear solve did not converge due to DIVERGED_INDEFINITE_PC
>> >> iterations 1
>> >>
>> >> I also try adding "-sub_pc_factor_shift_nonzero 0.0000000001" but the
>> >> CG case still fails.
>> >>
>> >> Am I missing some step in handling the null space when using CG?
>> >>
>> >> Thanks,
>> >>
>> >> Shao-Ching Huang
>> >>
>> >>
>>
>>
>>
>>
>> --
>> Pang Shengyong
>> Solidification Simulation Lab,
>> State Key Lab of Mould & Die Technology,
>> Huazhong Univ. of Sci. & Tech. China
>>
>
>


-- 
Pang Shengyong
Solidification Simulation Lab,
State Key Lab of Mould & Die Technology,
Huazhong Univ. of Sci. & Tech. China
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