# solving a particular linear equation system

Barry Smith bsmith at mcs.anl.gov
Fri May 15 17:13:20 CDT 2009

```   Note that even in these cases the resulting residual norm is very
large, relative to 1.e-14.

You might try superlu (not superlu_dist) it tries hard to do enough
pivoting to generate an accurate answer.

Barry

On May 15, 2009, at 5:10 PM, Jed Brown wrote:

> Matthew Knepley wrote:
>> I do not think its fine. I ran with KSP ex10:
>>
>> knepley at khan:/PETSc3/petsc/petsc-dev/src/ksp/ksp/examples/tutorials
>> \$ ./ex10
>> -f0 ~/Desktop/binaryoutput -ksp_monitor -pc_type lu -ksp_type preonly
>> Number of iterations =   1
>> Residual norm 1.12564e+06
>
> Interesting, this instability is highly dependent on the ordering
>
> \$ ./ex10 -f ~/dl/binaryoutput -ksp_converged_reason -
> ksp_monitor_singular_value -pc_type lu -pc_factor_mat_ordering_type
> rcm
>  0 KSP Residual norm 4.424612243135e+02 % max 1 min 1 max/min 1
>  1 KSP Residual norm 1.211880345965e-09 % max 1 min 1 max/min 1
> Linear solve converged due to CONVERGED_RTOL iterations 1
> Number of iterations =   1
> Residual norm 0.00398084
>
>
> also,
>
> \$ ./ex10 -f ~/dl/binaryoutput -ksp_converged_reason -pc_type lu -
> pc_factor_mat_solver_package umfpack
> Linear solve converged due to CONVERGED_RTOL iterations 2
> Number of iterations =   2
> Residual norm 0.0797212
>
> \$ ./ex10 -f ~/dl/binaryoutput -ksp_converged_reason -pc_type lu -
> pc_factor_mat_solver_package mumps
> Linear solve converged due to CONVERGED_RTOL iterations 1
> Number of iterations =   1
> Residual norm 0.00322144
>
>
> I agree with Matt about trying to reformulate the problem, at least if
> you need a scalable preconditioner.
>
> Jed
>

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