solving a particular linear equation system

[Jed Brown]

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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