solving a particular linear equation system

[Matthew Knepley]

On Fri, May 15, 2009 at 2:29 PM, Christian May <cmay at phys.ethz.ch> wrote:

> Hi everybody,
>
> I have trouble solving a linear equation system with PETSc 3.0.0.
> I tried the following combinations of solvers and preconditioners and list
> the results:
>
> cg+sor:       Linear solve did not converge due to DIVERGED_NAN
> cg+bjacobi:   Linear solve did not converge due to DIVERGED_INDEFINITE_PC
> cg+ilu:       Linear solve did not converge due to DIVERGED_INDEFINITE_MAT
>

1) This  matrix is not SPD


> gmres+sor:    Linear solve did not converge due to DIVERGED_NAN
> gmres+bjacobi:Linear solve did not converge due to DIVERGED_ITS
> gmres+ilu:    Linear solve did not converge due to DIVERGED_ITS


2) From DIVERGED_NAN, there is either a bug in the code, or you had some
sort of floating point badness from excessive iteration. I think the former.

3) Run with -pc_type lu -ksp_type preonly first to test.

4) If you need parallelism with such an ill-conditioned matrix, you can try
MUMPS

  Matt


> It might be that the matrix is not positive definite, which explains some
> of the problems. In the last two cases it kind of works, but convergence is
> horribly slow and it aborts after 10000 iterations.
>
> If somebody could please have a look at the matrix and the right hand side
> vector, I've put them here:
> http://www.mayarea.de/download/small_matrix.tgz
> The archive contains a file named A.txt, consisting of three columns
> i j Aij and a file b.txt with two columns i and bi.
>
> Any hint on how to solve this linear equation system (in reasonable time)
> is appreciated.
>
> Thanks a lot in advance!
>
> Christian
>
-- 
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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